Semi-empirical mass formula

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In nuclear physics, the semi-empirical mass formula (SEMF) (sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approximate the mass and various other properties of an atomic nucleus from its number of protons and neutrons. As the name suggests, it is based partly on theory and partly on empirical measurements. The formula represents the liquid drop model proposed by George Gamow, which can account for most of the terms in the formula and gives rough estimates for the values of the coefficients. It was first formulated in 1935 by German physicist Carl Friedrich von Weizsäcker and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today.

The formula gives a good approximation for atomic masses and thereby other effects. However, it fails to explain the existence of lines of greater binding energy at certain numbers of protons and neutrons. These numbers, known as magic numbers, are the foundation of the nuclear shell model.

The liquid drop model

Illustration of the terms of the semi-empirical mass formula in the liquid drop model of the atomic nucleus.

The liquid drop model was first proposed by George Gamow and further developed by Niels Bohr and John Archibald Wheeler. It treats the nucleus as a drop of incompressible fluid of very high density, held together by the nuclear force (a residual effect of the strong force), there is a similarity to the structure of a spherical liquid drop. While a crude model, the liquid drop model accounts for the spherical shape of most nuclei and makes a rough prediction of binding energy.

The corresponding mass formula is defined purely in terms of the numbers of protons and neutrons it contains. The original Weizsäcker formula defines five terms:

• Volume energy, when an assembly of nucleons of the same size is packed together into the smallest volume, each interior nucleon has a certain number of other nucleons in contact with it. So, this nuclear energy is proportional to the volume.
• Surface energy corrects for the previous assumption made that every nucleon interacts with the same number of other nucleons. This term is negative and proportional to the surface area, and is therefore roughly equivalent to liquid surface tension.
• Coulomb energy, the potential energy from each pair of protons. As this is a repulsive force, the binding energy is reduced.
• Asymmetry energy (also called Pauli Energy), which accounts for the Pauli exclusion principle. Unequal numbers of neutrons and protons imply filling higher energy levels for one type of particle, while leaving lower energy levels vacant for the other type.
• Pairing energy, which accounts for the tendency of proton pairs and neutron pairs to occur. An even number of particles is more stable than an odd number due to spin coupling.

The formula

The binding energy per nucleon (in MeV) shown as a function of the neutron number N and atomic number Z as given by the semi-empirical mass formula. A dashed line is included to show nuclides that have been discovered by experiment.

 

The difference between the energies predicted and that of known binding energies, given in kiloelectronvolts. Phenomena present can be explained by further subtle terms, but the mass formula cannot explain the presence of lines, clearly identifiable by sharp peaks in contours.

The mass of an atomic nucleus, for ${\displaystyle N}$ neutrons, ${\displaystyle Z}$ protons, and therefore ${\displaystyle A=N+Z}$ nucleons, is given by

${\displaystyle m=Zm_{\rm {p}}+Nm_{\rm {n}}-{\frac {E_{\rm {B}}(N,Z)}{c^{2}}}}$

where ${\displaystyle m_{\rm {p}}}$ and ${\displaystyle m_{\rm {n}}}$ are the rest mass of a proton and a neutron, respectively, and ${\displaystyle E_{\rm {B}}}$ is the binding energy of the nucleus. The semi-empirical mass formula states the binding energy is:

${\displaystyle E_{\rm {B}}=a_{\rm {V}}A-a_{\rm {S}}A^{2/3}-a_{\rm {C}}{\frac {Z(Z-1)}{A^{1/3}}}-a_{\rm {A}}{\frac {(N-Z)^{2}}{A}}+\delta (N,Z)}$

The ${\displaystyle \delta (N,Z)}$ term is either zero or ${\displaystyle \pm \delta _{0}}$, depending on the parity of ${\displaystyle N}$ and ${\displaystyle Z}$, where ${\displaystyle \delta _{0}={a_{\rm {P}}}{A^{k_{\rm {P}}}}}$ for some exponent ${\displaystyle k_{\rm {P}}}$. Note that as ${\displaystyle A=N+Z}$, the numerator of the ${\displaystyle a_{\rm {A}}}$ term can be rewritten as ${\displaystyle (A-2Z)^{2}}$.

Each of the terms in this formula has a theoretical basis. The coefficients ${\displaystyle a_{\rm {V}}}$, ${\displaystyle a_{\rm {S}}}$, ${\displaystyle a_{\rm {C}}}$, ${\displaystyle a_{\rm {A}}}$, and ${\displaystyle a_{\rm {P}}}$ are determined empirically; while they may be derived from experiment, they are typically derived from least squares fit to contemporary data. While typically expressed by its basic five terms, further terms exist to explain additional phenomena. Akin to how changing a polynomial fit will change its coefficients, the interplay between these coefficients as new phenomena are introduced is complex; some terms influence each other, whereas the ${\displaystyle a_{\rm {P}}}$ term is largely independent.

Volume term

The term ${\displaystyle a_{\rm {V}}A}$ is known as the volume term. The volume of the nucleus is proportional to A, so this term is proportional to the volume, hence the name.

The basis for this term is the strong nuclear force. The strong force affects both protons and neutrons, and as expected, this term is independent of Z. Because the number of pairs that can be taken from A particles is ${\displaystyle {\frac {A(A-1)}{2}}}$, one might expect a term proportional to ${\displaystyle A^{2}}$. However, the strong force has a very limited range, and a given nucleon may only interact strongly with its nearest neighbors and next nearest neighbors. Therefore, the number of pairs of particles that actually interact is roughly proportional to A, giving the volume term its form.

The coefficient ${\displaystyle a_{\rm {V}}}$ is smaller than the binding energy possessed by the nucleons with respect to their neighbors (${\displaystyle E_{\rm {b}}}$), which is of order of 40 MeV. This is because the larger the number of nucleons in the nucleus, the larger their kinetic energy is, due to the Pauli exclusion principle. If one treats the nucleus as a Fermi ball of ${\displaystyle A}$ nucleons, with equal numbers of protons and neutrons, then the total kinetic energy is ${\displaystyle {3 \over 5}A\varepsilon _{\rm {F}}}$, with ${\displaystyle \varepsilon _{\rm {F}}}$ the Fermi energy which is estimated as 38 MeV. Thus the expected value of ${\displaystyle a_{\rm {V}}}$ in this model is ${\displaystyle E_{\rm {b}}-{3 \over 5}\varepsilon _{\rm {F}}\sim 17\;\mathrm {MeV} }$, not far from the measured value.

Surface term

The term ${\displaystyle a_{\rm {S}}A^{2/3}}$ is known as the surface term. This term, also based on the strong force, is a correction to the volume term.

The volume term suggests that each nucleon interacts with a constant number of nucleons, independent of A. While this is very nearly true for nucleons deep within the nucleus, those nucleons on the surface of the nucleus have fewer nearest neighbors, justifying this correction. This can also be thought of as a surface tension term, and indeed a similar mechanism creates surface tension in liquids.

If the volume of the nucleus is proportional to A, then the radius should be proportional to ${\displaystyle A^{1/3}}$ and the surface area to ${\displaystyle A^{2/3}}$. This explains why the surface term is proportional to ${\displaystyle A^{2/3}}$. It can also be deduced that ${\displaystyle a_{\rm {S}}}$ should have a similar order of magnitude to ${\displaystyle a_{\rm {V}}}$.

Coulomb term

The term ${\displaystyle a_{\rm {C}}{\frac {Z(Z-1)}{A^{1/3}}}}$ or ${\displaystyle a_{\rm {C}}{\frac {Z^{2}}{A^{1/3}}}}$ is known as the Coulomb or electrostatic term.

The basis for this term is the electrostatic repulsion between protons. To a very rough approximation, the nucleus can be considered a sphere of uniform charge density. The potential energy of such a charge distribution can be shown to be

${\displaystyle E={\frac {3}{5}}\left({\frac {1}{4\pi \varepsilon _{0}}}\right){\frac {Q^{2}}{R}}}$

where Q is the total charge and R is the radius of the sphere. The value of ${\displaystyle a_{\rm {C}}}$ can be approximately calculated by using this equation to calculate the potential energy, using an empirical nuclear radius of ${\displaystyle R\approx r_{0}A^{\frac {1}{3}}}$ and Q=Ze. However, because electrostatic repulsion will only exist for more than one proton, ${\displaystyle Z^{2}}$ becomes ${\displaystyle Z(Z-1)}$:

${\displaystyle E={\frac {3}{5}}\left({\frac {1}{4\pi \varepsilon _{0}}}\right){\frac {Q^{2}}{R}}={\frac {3}{5}}\left({\frac {1}{4\pi \varepsilon _{0}}}\right){\frac {(Ze)^{2}}{(r_{0}A^{\frac {1}{3}})}}={\frac {3e^{2}Z^{2}}{20\pi \varepsilon _{0}r_{0}A^{\frac {1}{3}}}}\approx {\frac {3e^{2}Z(Z-1)}{20\pi \varepsilon _{0}r_{0}A^{\frac {1}{3}}}}=a_{\rm {C}}{\frac {Z(Z-1)}{A^{1/3}}}}$

where now the electrostatic Coulomb constant ${\displaystyle a_{\rm {C}}}$ is

${\displaystyle a_{\rm {C}}={\frac {3e^{2}}{20\pi \varepsilon _{0}r_{0}}}}$.

Using the fine-structure constant, we can rewrite the value of ${\displaystyle a_{\rm {C}}}$:

${\displaystyle a_{\rm {C}}={\frac {3}{5}}\left({\frac {\hbar c\alpha }{r_{0}}}\right)={\frac {3}{5}}\left({\frac {R_{\rm {P}}}{r_{0}}}\right)\alpha m_{\rm {p}}c^{2}}$

where ${\displaystyle \alpha }$ is the fine-structure constant and ${\displaystyle r_{0}A^{1/3}}$ is the radius of a nucleus, giving ${\displaystyle r_{0}}$ to be approximately 1.25 femtometers. ${\displaystyle R_{\rm {P}}}$ is the proton reduced Compton wavelength, and ${\displaystyle m_{\rm {p}}}$ is the proton mass. This gives ${\displaystyle a_{\rm {C}}}$ an approximate theoretical value of 0.691 MeV, not far from the measured value.

Asymmetry term

The term ${\displaystyle a_{\rm {A}}{\frac {(N-Z)^{2}}{A}}}$ is known as the asymmetry term (or Pauli term).

The theoretical justification for this term is more complex. The Pauli exclusion principle states that no two identical fermions can occupy exactly the same quantum state in an atom. At a given energy level, there are only finitely many quantum states available for particles. What this means in the nucleus is that as more particles are "added", these particles must occupy higher energy levels, increasing the total energy of the nucleus (and decreasing the binding energy). Note that this effect is not based on any of the fundamental forces (gravitational, electromagnetic, etc.), only the Pauli exclusion principle.

Protons and neutrons, being distinct types of particles, occupy different quantum states. One can think of two different "pools" of states, one for protons and one for neutrons. Now, for example, if there are significantly more neutrons than protons in a nucleus, some of the neutrons will be higher in energy than the available states in the proton pool. If we could move some particles from the neutron pool to the proton pool, in other words change some neutrons into protons, we would significantly decrease the energy. The imbalance between the number of protons and neutrons causes the energy to be higher than it needs to be, for a given number of nucleons. This is the basis for the asymmetry term.

The actual form of the asymmetry term can again be derived by modeling the nucleus as a Fermi ball of protons and neutrons. Its total kinetic energy is

${\displaystyle E_{\rm {k}}={3 \over 5}(Z{\varepsilon _{\rm {F}}}_{\rm {p}}+N{\varepsilon _{\rm {F}}}_{\rm {n}})}$

where ${\displaystyle {\varepsilon _{\rm {F}}}_{\rm {p}}}$ and ${\displaystyle {\varepsilon _{\rm {F}}}_{\rm {n}}}$ are the Fermi energies of the protons and neutrons. Since these are proportional to ${\displaystyle Z^{2/3}}$ and ${\displaystyle N^{2/3}}$, respectively, one gets

${\displaystyle E_{\rm {k}}=C(Z^{5/3}+N^{5/3})}$ for some constant C.

The leading terms in the expansion in the difference ${\displaystyle N-Z}$ are then

${\displaystyle E_{\rm {k}}={C \over 2^{2/3}}\left(A^{5/3}+{5 \over 9}{(N-Z)^{2} \over A^{1/3}}\right)+O((N-Z)^{4}).}$

At the zeroth order in the expansion the kinetic energy is just the overall Fermi energy ${\displaystyle \varepsilon _{\rm {F}}\equiv {\varepsilon _{\rm {F}}}_{\rm {p}}={\varepsilon _{\rm {F}}}_{\rm {n}}}$ multiplied by ${\displaystyle {3 \over 5}A}$. Thus we get

${\displaystyle E_{\rm {k}}={3 \over 5}\varepsilon _{\rm {F}}A+{1 \over 3}\varepsilon _{\rm {F}}{(N-Z)^{2} \over A}+O((N-Z)^{4}).}$

The first term contributes to the volume term in the semi-empirical mass formula, and the second term is minus the asymmetry term (remember the kinetic energy contributes to the total binding energy with a negative sign).

${\displaystyle \varepsilon _{\rm {F}}}$ is 38 MeV, so calculating ${\displaystyle a_{\rm {A}}}$ from the equation above, we get only half the measured value. The discrepancy is explained by our model not being accurate: nucleons in fact interact with each other, and are not spread evenly across the nucleus. For example, in the shell model, a proton and a neutron with overlapping wavefunctions will have a greater strong interaction between them and stronger binding energy. This makes it energetically favourable (i.e. having lower energy) for protons and neutrons to have the same quantum numbers (other than isospin), and thus increase the energy cost of asymmetry between them.

One can also understand the asymmetry term intuitively, as follows. It should be dependent on the absolute difference ${\displaystyle |N-Z|}$, and the form ${\displaystyle (N-Z)^{2}}$ is simple and differentiable, which is important for certain applications of the formula. In addition, small differences between Z and N do not have a high energy cost. The A in the denominator reflects the fact that a given difference ${\displaystyle |N-Z|}$ is less significant for larger values of A.

Pairing term

Magnitude of the pairing term in the total binding energy for even-even and odd-odd nuclei, as a function of mass number. Two fits are shown (blue and red line). The pairing term (positive for even-even and negative for odd-odd nuclei) was derived from the binding energy data in: G. Audi et al., 'The AME2012 atomic mass evaluation', in Chinese Physics C 36 (2012/12) pp. 1287–1602.

The term ${\displaystyle \delta (A,Z)}$ is known as the pairing term (possibly also known as the pairwise interaction). This term captures the effect of spin-coupling. It is given by:

${\displaystyle \delta (A,Z)={\begin{cases}+\delta _{0}&Z,N{\text{ even }}(A{\text{ even}})\\0&A{\text{ odd}}\\-\delta _{0}&Z,N{\text{ odd }}(A{\text{ even}})\end{cases}}}$

where ${\displaystyle \delta _{0}}$ is found empirically to have a value of about 1000 keV, slowly decreasing with mass number A. The binding energy may be increased by converting one of the odd protons or neutrons into a neutron or proton so the odd nucleon can form a pair with its odd neighbour forming and even Z, N. The pair have overlapping wave functions and sit very close together with a bond stronger than any other configuration. When the pairing term is substituted into the binding energy equation, for even Z, N, the pairing term adds binding energy and for odd Z, N the pairing term removes binding energy.

The dependence on mass number is commonly parametrized as

${\displaystyle \delta _{0}={a_{\rm {P}}}{A^{k_{\rm {P}}}}.}$

The value of the exponent k_P is determined from experimental binding energy data. In the past its value was often assumed to be −3/4, but modern experimental data indicate that a value of −1/2 is nearer the mark:

${\displaystyle \delta _{0}={a_{\rm {P}}}{A^{-1/2}}}$ or ${\displaystyle \delta _{0}={a_{\rm {P}}}{A^{-3/4}}}$.

Due to the Pauli exclusion principle the nucleus would have a lower energy if the number of protons with spin up were equal to the number of protons with spin down. This is also true for neutrons. Only if both Z and N are even can both protons and neutrons have equal numbers of spin up and spin down particles. This is a similar effect to the asymmetry term.

The factor ${\displaystyle A^{k_{\rm {P}}}}$ is not easily explained theoretically. The Fermi ball calculation we have used above, based on the liquid drop model but neglecting interactions, will give an ${\displaystyle A^{-1}}$ dependence, as in the asymmetry term. This means that the actual effect for large nuclei will be larger than expected by that model. This should be explained by the interactions between nucleons; For example, in the shell model, two protons with the same quantum numbers (other than spin) will have completely overlapping wavefunctions and will thus have greater strong interaction between them and stronger binding energy. This makes it energetically favourable (i.e. having lower energy) for protons to form pairs of opposite spin. The same is true for neutrons.

Calculating the coefficients

The coefficients are calculated by fitting to experimentally measured masses of nuclei. Their values can vary depending on how they are fitted to the data and which unit is used to express the mass. Several examples are as shown below.

	Eisberg & Resnick	Least-squares fit (1)	Least-squares fit (2)	Rohlf	Wapstra
unit	u	MeV	MeV	MeV	MeV
${\displaystyle a_{\rm {V}}}$	0.01691	15.8	15.76	15.75	14.1
${\displaystyle a_{\rm {S}}}$	0.01911	18.3	17.81	17.8	13
${\displaystyle a_{\rm {C}}}$	0.000673	0.714	0.711	0.711	0.595
${\displaystyle a_{\rm {A}}}$	0.10175	23.2	23.702	23.7	19
${\displaystyle a_{\rm {P}}}$	0.012	12	34	11.18	33.5
${\displaystyle k_{\rm {P}}}$	−1/2	−1/2	−3/4	−1/2	−3/4
${\displaystyle \delta _{0}}$ (even-even)	${\displaystyle -0.012 \over A^{1/2}}$	${\displaystyle +12 \over A^{1/2}}$	${\displaystyle +34 \over A^{3/4}}$	${\displaystyle +11.18 \over A^{1/2}}$	${\displaystyle +33.5 \over A^{3/4}}$
${\displaystyle \delta _{0}}$ (odd-odd)	${\displaystyle +0.012 \over A^{1/2}}$	${\displaystyle -12 \over A^{1/2}}$	${\displaystyle -34 \over A^{3/4}}$	${\displaystyle -11.18 \over A^{1/2}}$	${\displaystyle -33.5 \over A^{3/4}}$
${\displaystyle \delta _{0}}$ (even-odd, odd-even)	0	0	0	0	0

This model uses ${\displaystyle (Z-A/2)^{2}}$ in the numerator of the Asymmetry term.

The formula does not consider the internal shell structure of the nucleus.

The semi-empirical mass formula therefore provides a good fit to heavier nuclei, and a poor fit to very light nuclei, especially ⁴He. For light nuclei, it is usually better to use a model that takes this shell structure into account.

Examples of consequences of the formula

By maximizing E_b(A,Z) with respect to Z, one would find the best neutron–proton ratio N/Z for a given atomic weight A. We get

${\displaystyle N/Z\approx 1+{\frac {a_{\rm {C}}}{2a_{\rm {A}}}}A^{2/3}.}$

This is roughly 1 for light nuclei, but for heavy nuclei the ratio grows in good agreement with experiment.

By substituting the above value of Z back into E_b, one obtains the binding energy as a function of the atomic weight, E_b(A). Maximizing E_b(A) /A with respect to A gives the nucleus which is most strongly bound, i.e. most stable. The value we get is A = 63 (copper), close to the measured values of A = 62 (nickel) and A = 58 (iron).

The liquid drop model also allows the computation of fission barriers for nuclei, which determine the stability of a nucleus against spontaneous fission. It was originally speculated that elements beyond atomic number 104 could not exist, as they would undergo fission with very short half-lives, though this formula did not consider stabilizing effects of closed nuclear shells. A modified formula considering shell effects reproduces known data and the predicted island of stability (in which fission barriers and half-lives are expected to increase, reaching a maximum at the shell closures), though also suggests a possible limit to existence of superheavy nuclei beyond Z = 120 and N = 184.

This model uses ${\displaystyle Z^{2}}$ in the numerator of the Coulomb term.

Spacecraft electric propulsion

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https://en.wikipedia.org/wiki/Spacecraft_electric_propulsion 

 

6 kW Hall thruster in operation at the NASA Jet Propulsion Laboratory

Spacecraft electric propulsion (or just electric propulsion) is a type of spacecraft propulsion technique that uses electrostatic or electromagnetic fields to accelerate mass to high speed and thus generate thrust to modify the velocity of a spacecraft in orbit.

Electric thrusters typically use much less propellant than chemical rockets because they have a higher exhaust speed (operate at a higher specific impulse) than chemical rockets. Due to limited electric power the thrust is much weaker compared to chemical rockets, but electric propulsion can provide thrust for a longer time.

Electric propulsion was first successfully demonstrated by NASA and is now a mature and widely used technology on spacecraft. American and Russian satellites have used electric propulsion for decades. As of 2019, over 500 spacecraft operated throughout the Solar System use electric propulsion for station keeping, orbit raising, or primary propulsion. In the future, the most advanced electric thrusters may be able to impart a delta-v of 100 km/s (62 mi/s), which is enough to take a spacecraft to the outer planets of the Solar System (with nuclear power), but is insufficient for interstellar travel. An electric rocket with an external power source (transmissible through laser on the photovoltaic panels) has a theoretical possibility for interstellar flight. However, electric propulsion is not suitable for launches from the Earth's surface, as it offers too little thrust.

On a journey to Mars, an electrically powered ship might be able to carry 70% of its initial mass to the destination, while a chemical rocket could carry only a few percent.

History

The idea of electric propulsion for spacecraft was introduced in 1911 by Konstantin Tsiolkovsky. Earlier, Robert Goddard had noted such a possibility in his personal notebook.

Electrically powered propulsion with a nuclear reactor was considered by Tony Martin for interstellar Project Daedalus in 1973, but the approach was rejected because of its thrust profile, the weight of equipment needed to convert nuclear energy into electricity, and as a result a small acceleration, which would take a century to achieve the desired speed.

The first demonstration of electric propulsion was an ion engine carried on board the NASA SERT-1 (Space Electric Rocket Test) spacecraft. It launched on 20 July 1964 and operated for 31 minutes. A follow-up mission launched on 3 February 1970, SERT-2. It carried two ion thrusters, one operated for more than five months and the other for almost three months.

By the early 2010s, many satellite manufacturers were offering electric propulsion options on their satellites—mostly for on-orbit attitude control—while some commercial communication satellite operators were beginning to use them for geosynchronous orbit insertion in place of traditional chemical rocket engines.

Types

Ion and plasma drives

These types of rocket-like reaction engines use electric energy to obtain thrust from propellant. Unlike rocket engines, these kinds of engines do not require nozzles, and thus are not considered true rockets.

Electric propulsion thrusters for spacecraft may be grouped into three families based on the type of force used to accelerate the ions of the plasma:

Electrostatic

Main article: Ion thruster

If the acceleration is caused mainly by the Coulomb force (i.e. application of a static electric field in the direction of the acceleration) the device is considered electrostatic. Types:

• Gridded ion thruster
  • NASA Solar Technology Application Readiness (NSTAR)
  • HiPEP
  • Radiofrequency ion thruster
• Hall-effect thruster, including its subtypes Stationary Plasma Thruster (SPT) and Thruster with Anode Layer (TAL)
• Colloid ion thruster
• Field emission electric propulsion
• Nano-particle field extraction thruster

Electrothermal

The electrothermal category groups devices that use electromagnetic fields to generate a plasma to increase the temperature of the bulk propellant. The thermal energy imparted to the propellant gas is then converted into kinetic energy by a nozzle of either solid material or magnetic fields. Low molecular weight gases (e.g. hydrogen, helium, ammonia) are preferred propellants for this kind of system.

An electrothermal engine uses a nozzle to convert heat into linear motion, so it is a true rocket even though the energy producing the heat comes from an external source.

Performance of electrothermal systems in terms of specific impulse (Isp) is 500 to ~1000 seconds, but exceeds that of cold gas thrusters, monopropellant rockets, and even most bipropellant rockets. In the USSR, electrothermal engines entered use in 1971; the Soviet "Meteor-3", "Meteor-Priroda", "Resurs-O" satellite series and the Russian "Elektro" satellite are equipped with them. Electrothermal systems by Aerojet (MR-510) are currently used on Lockheed Martin A2100 satellites using hydrazine as a propellant.

• Resistojet
• Arcjet
• Microwave
• Variable specific impulse magnetoplasma rocket (VASIMR)

Electromagnetic

Main article: Plasma propulsion engine

Electromagnetic thrusters accelerate ions either by the Lorentz force or by the effect of electromagnetic fields where the electric field is not in the direction of the acceleration. Types:

• Electrodeless plasma thruster
• Magnetoplasmadynamic thruster
• Pulsed inductive thruster
• Pulsed plasma thruster
• Helicon Double Layer Thruster

Non-ion drives

Photonic

See also: Laser propulsion and Photon rocket

A photonic drive interacts only with photons.

Electrodynamic tether

Main article: Electrodynamic tether

Electrodynamic tethers are long conducting wires, such as one deployed from a tether satellite, which can operate on electromagnetic principles as generators, by converting their kinetic energy to electric energy, or as motors, converting electric energy to kinetic energy. Electric potential is generated across a conductive tether by its motion through the Earth's magnetic field. The choice of the metal conductor to be used in an electrodynamic tether is determined by factors such as electrical conductivity, and density. Secondary factors, depending on the application, include cost, strength, and melting point.

Controversial

Some proposed propulsion methods apparently violate currently-understood laws of physics, including:

• Quantum Vacuum Thruster
• EM Drive or Cannae Drive

Steady vs. unsteady

Electric propulsion systems can be characterized as either steady (continuous firing for a prescribed duration) or unsteady (pulsed firings accumulating to a desired impulse). These classifications can be applied to all types of propulsion engines.

Dynamic properties

Further information: Reaction engine § Energy use

Electrically powered rocket engines provide lower thrust compared to chemical rockets by several orders of magnitude because of the limited electrical power available in a spacecraft. A chemical rocket imparts energy to the combustion products directly, whereas an electrical system requires several steps. However, the high velocity and lower reaction mass expended for the same thrust allows electric rockets to run on less fuel. This differs from the typical chemical-powered spacecraft, where the engines require more fuel, requiring the spacecraft to mostly follow an inertial trajectory. When near a planet, low-thrust propulsion may not offset the gravitational force. An electric rocket engine cannot provide enough thrust to lift the vehicle from a planet's surface, but a low thrust applied for a long interval can allow a spacecraft to maneuver near a planet.

Project Orion (nuclear propulsion)

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion) 

Artist's conception of the NASA reference design for the Project Orion starship powered by nuclear propulsion

Project Orion was a study conducted between the 1950s and 1960s by the United States Air Force, DARPA, and NASA for the purpose of identifying the efficacy of a starship directly propelled by a series of explosions of atomic bombs behind the craft via nuclear pulse propulsion. Early versions of this vehicle were proposed to take off from the ground; later versions were presented for use only in space. Six non-nuclear tests were conducted using models. The project was eventually abandoned for multiple reasons, such as the Partial Test Ban Treaty, which banned nuclear explosions in space, as well as concerns over nuclear fallout.

The idea of rocket propulsion by combustion of explosive substance was first proposed by Russian explosives expert Nikolai Kibalchich in 1881, and in 1891 similar ideas were developed independently by German engineer Hermann Ganswindt. Robert A. Heinlein mentions powering spaceships with nuclear bombs in his 1940 short story "Blowups Happen." Real life proposals of nuclear propulsion were first made by Stanislaw Ulam in 1946, and preliminary calculations were made by F. Reines and Ulam in a Los Alamos memorandum dated 1947. The actual project, initiated in 1958, was led by Ted Taylor at General Atomics and physicist Freeman Dyson, who at Taylor's request took a year away from the Institute for Advanced Study in Princeton to work on the project.

The Orion concept offered high thrust and high specific impulse, or propellant efficiency, at the same time. The unprecedented extreme power requirements for doing so would be met by nuclear explosions, of such power relative to the vehicle's mass as to be survived only by using external detonations without attempting to contain them in internal structures. As a qualitative comparison, traditional chemical rockets—such as the Saturn V that took the Apollo program to the Moon—produce high thrust with low specific impulse, whereas electric ion engines produce a small amount of thrust very efficiently. Orion would have offered performance greater than the most advanced conventional or nuclear rocket engines then under consideration. Supporters of Project Orion felt that it had potential for cheap interplanetary travel, but it lost political approval over concerns about fallout from its propulsion.

The Partial Test Ban Treaty of 1963 is generally acknowledged to have ended the project. However, from Project Longshot to Project Daedalus, Mini-Mag Orion, and other proposals which reach engineering analysis at the level of considering thermal power dissipation, the principle of external nuclear pulse propulsion to maximize survivable power has remained common among serious concepts for interstellar flight without external power beaming and for very high-performance interplanetary flight. Such later proposals have tended to modify the basic principle by envisioning equipment driving detonation of much smaller fission or fusion pellets, in contrast to Project Orion's larger nuclear pulse units (full nuclear bombs) based on less speculative technology.

Basic principles

The Orion Spacecraft – key components

The Orion nuclear pulse drive combines a very high exhaust velocity, from 19 to 31 km/s (12 to 19 mi/s) in typical interplanetary designs, with meganewtons of thrust. Many spacecraft propulsion drives can achieve one of these or the other, but nuclear pulse rockets are the only proposed technology that could potentially meet the extreme power requirements to deliver both at once (see spacecraft propulsion for more speculative systems).

Specific impulse (I_sp) measures how much thrust can be derived from a given mass of fuel, and is a standard figure of merit for rocketry. For any rocket propulsion, since the kinetic energy of exhaust goes up with velocity squared (kinetic energy = ½ mv²), whereas the momentum and thrust go up with velocity linearly (momentum = mv), obtaining a particular level of thrust (as in a number of g acceleration) requires far more power each time that exhaust velocity and I_sp are much increased in a design goal. (For instance, the most fundamental reason that current and proposed electric propulsion systems of high I_sp tend to be low thrust is due to their limits on available power. Their thrust is actually inversely proportional to I_sp if power going into exhaust is constant or at its limit from heat dissipation needs or other engineering constraints.) The Orion concept detonates nuclear explosions externally at a rate of power release which is beyond what nuclear reactors could survive internally with known materials and design.

Since weight is no limitation, an Orion craft can be extremely robust. An uncrewed craft could tolerate very large accelerations, perhaps 100 g. A human-crewed Orion, however, must use some sort of damping system behind the pusher plate to smooth the near instantaneous acceleration to a level that humans can comfortably withstand – typically about 2 to 4 g.

The high performance depends on the high exhaust velocity, in order to maximize the rocket's force for a given mass of propellant. The velocity of the plasma debris is proportional to the square root of the change in the temperature (T_c) of the nuclear fireball. Since such fireballs typically achieve ten million degrees Celsius or more in less than a millisecond, they create very high velocities. However, a practical design must also limit the destructive radius of the fireball. The diameter of the nuclear fireball is proportional to the square root of the bomb's explosive yield.

The shape of the bomb's reaction mass is critical to efficiency. The original project designed bombs with a reaction mass made of tungsten. The bomb's geometry and materials focused the X-rays and plasma from the core of nuclear explosive to hit the reaction mass. In effect each bomb would be a nuclear shaped charge.

A bomb with a cylinder of reaction mass expands into a flat, disk-shaped wave of plasma when it explodes. A bomb with a disk-shaped reaction mass expands into a far more efficient cigar-shaped wave of plasma debris. The cigar shape focuses much of the plasma to impinge onto the pusher-plate. For greatest mission efficiency the rocket equation demands that the greatest fraction of the bomb's explosive force be directed at the spacecraft, rather than being spent isotropically.

The maximum effective specific impulse, I_sp, of an Orion nuclear pulse drive generally is equal to:

${\displaystyle I_{sp}={\frac {C_{0}\cdot V_{e}}{g_{n}}}}$

where C₀ is the collimation factor (what fraction of the explosion plasma debris will actually hit the impulse absorber plate when a pulse unit explodes), V_e is the nuclear pulse unit plasma debris velocity, and g_n is the standard acceleration of gravity (9.81 m/s²; this factor is not necessary if I_sp is measured in N·s/kg or m/s). A collimation factor of nearly 0.5 can be achieved by matching the diameter of the pusher plate to the diameter of the nuclear fireball created by the explosion of a nuclear pulse unit.

The smaller the bomb, the smaller each impulse will be, so the higher the rate of impulses and more than will be needed to achieve orbit. Smaller impulses also mean less g shock on the pusher plate and less need for damping to smooth out the acceleration.

The optimal Orion drive bomblet yield (for the human crewed 4,000 ton reference design) was calculated to be in the region of 0.15 kt, with approx 800 bombs needed to orbit and a bomb rate of approx 1 per second.

Sizes of vehicles

The following can be found in George Dyson's book. The figures for the comparison with Saturn V are taken from this section and converted from metric (kg) to US short tons (abbreviated "t" here).

Image of the smallest Orion vehicle extensively studied, which could have had a payload of around 100 tonnes in an 8 crew round trip to Mars. On the left, the 10 meter diameter Saturn V "Boost-to-orbit" variant, requiring in-orbit assembly before the Orion vehicle would be capable of moving under its own propulsion system. On the far right, the fully assembled "lofting" configuration, in which the spacecraft would be lifted high into the atmosphere before pulse propulsion began. As depicted in the 1964 NASA document "Nuclear Pulse Space Vehicle Study Vol III - Conceptual Vehicle Designs and Operational Systems."

 

	Orbital test	Interplanetary	Advanced interplanetary	Saturn V
Ship mass	880 t	4,000 t	10,000 t	3,350 t
Ship diameter	25 m	40 m	56 m	10 m
Ship height	36 m	60 m	85 m	110 m
Bomb yield (sea level)	0.03 kt	0.14 kt	0.35 kt	n/a
Bombs (to 300 mi Low Earth Orbit)	800	800	800	n/a
Payload (to 300 mi LEO)	300 t	1,600 t	6,100 t	130 t
Payload (to Moon soft landing)	170 t	1,200 t	5,700 t	2 t
Payload (Mars orbit return)	80 t	800 t	5,300 t	–
Payload (3 yr Saturn return)	–	–	1,300 t	–

In late 1958 to early 1959, it was realized that the smallest practical vehicle would be determined by the smallest achievable bomb yield. The use of 0.03 kt (sea-level yield) bombs would give vehicle mass of 880 tons. However, this was regarded as too small for anything other than an orbital test vehicle and the team soon focused on a 4,000 ton "base design".

At that time, the details of small bomb designs were shrouded in secrecy. Many Orion design reports had all details of bombs removed before release. Contrast the above details with the 1959 report by General Atomics, which explored the parameters of three different sizes of hypothetical Orion spacecraft:

	"Satellite" Orion	"Midrange" Orion	"Super" Orion
Ship diameter	17–20 m	40 m	400 m
Ship mass	300 t	1000–2000 t	8,000,000 t
Number of bombs	540	1080	1080
Individual bomb mass	0.22 t	0.37–0.75 t	3000 t

The biggest design above is the "super" Orion design; at 8 million tonnes, it could easily be a city. In interviews, the designers contemplated the large ship as a possible interstellar ark. This extreme design could be built with materials and techniques that could be obtained in 1958 or were anticipated to be available shortly after.

Most of the three thousand tonnes of each of the "super" Orion's propulsion units would be inert material such as polyethylene, or boron salts, used to transmit the force of the propulsion units detonation to the Orion's pusher plate, and absorb neutrons to minimize fallout. One design proposed by Freeman Dyson for the "Super Orion" called for the pusher plate to be composed primarily of uranium or a transuranic element so that upon reaching a nearby star system the plate could be converted to nuclear fuel.

Theoretical applications

The Orion nuclear pulse rocket design has extremely high performance. Orion nuclear pulse rockets using nuclear fission type pulse units were originally intended for use on interplanetary space flights.

Missions that were designed for an Orion vehicle in the original project included single stage (i.e., directly from Earth's surface) to Mars and back, and a trip to one of the moons of Saturn.

Freeman Dyson performed the first analysis of what kinds of Orion missions were possible to reach Alpha Centauri, the nearest star system to the Sun. His 1968 paper "Interstellar Transport" (Physics Today, October 1968, pp. 41–45) retained the concept of large nuclear explosions but Dyson moved away from the use of fission bombs and considered the use of one megaton deuterium fusion explosions instead. His conclusions were simple: the debris velocity of fusion explosions was probably in the 3000–30,000 km/s range and the reflecting geometry of Orion's hemispherical pusher plate would reduce that range to 750–15,000 km/s.

To estimate the upper and lower limits of what could be done using contemporary technology (in 1968), Dyson considered two starship designs. The more conservative energy limited pusher plate design simply had to absorb all the thermal energy of each impinging explosion (4×10¹⁵ joules, half of which would be absorbed by the pusher plate) without melting. Dyson estimated that if the exposed surface consisted of copper with a thickness of 1 mm, then the diameter and mass of the hemispherical pusher plate would have to be 20 kilometers and 5 million tonnes, respectively. 100 seconds would be required to allow the copper to radiatively cool before the next explosion. It would then take on the order of 1000 years for the energy-limited heat sink Orion design to reach Alpha Centauri.

In order to improve on this performance while reducing size and cost, Dyson also considered an alternative momentum limited pusher plate design where an ablation coating of the exposed surface is substituted to get rid of the excess heat. The limitation is then set by the capacity of shock absorbers to transfer momentum from the impulsively accelerated pusher plate to the smoothly accelerated vehicle. Dyson calculated that the properties of available materials limited the velocity transferred by each explosion to ~30 meters per second independent of the size and nature of the explosion. If the vehicle is to be accelerated at 1 Earth gravity (9.81 m/s²) with this velocity transfer, then the pulse rate is one explosion every three seconds. The dimensions and performance of Dyson's vehicles are given in the following table:

	"Energy Limited" Orion	"Momentum Limited" Orion
Ship diameter (meters)	20,000 m	100 m
Mass of empty ship (tonnes)	10,000,000 t (incl.5,000,000 t copper hemisphere)	100,000 t (incl. 50,000 t structure+payload)
+Number of bombs = total bomb mass (each 1 Mt bomb weighs 1 tonne)	30,000,000	300,000
=Departure mass (tonnes)	40,000,000 t	400,000 t
Maximum velocity (kilometers per second)	1000 km/s (=0.33% of the speed of light)	10,000 km/s (=3.3% of the speed of light)
Mean acceleration (Earth gravities)	0.00003 g (accelerate for 100 years)	1 g (accelerate for 10 days)
Time to Alpha Centauri (one way, no slow down)	1330 years	133 years
Estimated cost	1 year of U.S. GNP (1968), $3.67 Trillion	0.1 year of U.S. GNP $0.367 Trillion

Later studies indicate that the top cruise velocity that can theoretically be achieved are a few percent of the speed of light (0.08–0.1c). An atomic (fission) Orion can achieve perhaps 9%–11% of the speed of light. A nuclear pulse drive starship powered by fusion-antimatter catalyzed nuclear pulse propulsion units would be similarly in the 10% range and pure Matter-antimatter annihilation rockets would be theoretically capable of obtaining a velocity between 50% to 80% of the speed of light. In each case saving fuel for slowing down halves the maximum speed. The concept of using a magnetic sail to decelerate the spacecraft as it approaches its destination has been discussed as an alternative to using propellant; this would allow the ship to travel near the maximum theoretical velocity.

At 0.1c, Orion thermonuclear starships would require a flight time of at least 44 years to reach Alpha Centauri, not counting time needed to reach that speed (about 36 days at constant acceleration of 1g or 9.8 m/s²). At 0.1c, an Orion starship would require 100 years to travel 10 light years. The astronomer Carl Sagan suggested that this would be an excellent use for current stockpiles of nuclear weapons.

Further information: Interstellar travel

Later developments

Modern pulsed fission propulsion concept

A concept similar to Orion was designed by the British Interplanetary Society (B.I.S.) in the years 1973–1974. Project Daedalus was to be a robotic interstellar probe to Barnard's Star that would travel at 12% of the speed of light. In 1989, a similar concept was studied by the U.S. Navy and NASA in Project Longshot. Both of these concepts require significant advances in fusion technology, and therefore cannot be built at present, unlike Orion.

From 1998 to the present, the nuclear engineering department at Pennsylvania State University has been developing two improved versions of project Orion known as Project ICAN and Project AIMStar using compact antimatter catalyzed nuclear pulse propulsion units, rather than the large inertial confinement fusion ignition systems proposed in Project Daedalus and Longshot.

Costs

The expense of the fissionable materials required was thought to be high, until the physicist Ted Taylor showed that with the right designs for explosives, the amount of fissionables used on launch was close to constant for every size of Orion from 2,000 tons to 8,000,000 tons. The larger bombs used more explosives to super-compress the fissionables, increasing efficiency. The extra debris from the explosives also serves as additional propulsion mass.

The bulk of costs for historical nuclear defense programs have been for delivery and support systems, rather than for production cost of the bombs directly (with warheads being 7% of the U.S. 1946–1996 expense total according to one study). After initial infrastructure development and investment, the marginal cost of additional nuclear bombs in mass production can be relatively low. In the 1980s, some U.S. thermonuclear warheads had $1.1 million estimated cost each ($630 million for 560). For the perhaps simpler fission pulse units to be used by one Orion design, a 1964 source estimated a cost of $40000 or less each in mass production, which would be up to approximately $0.3 million each in modern-day dollars adjusted for inflation.

Project Daedalus later proposed fusion explosives (deuterium or tritium pellets) detonated by electron beam inertial confinement. This is the same principle behind inertial confinement fusion. Theoretically, it could be scaled down to far smaller explosions, and require small shock absorbers.

Vehicle architecture

A design for the Orion propulsion module

From 1957 to 1964 this information was used to design a spacecraft propulsion system called Orion, in which nuclear explosives would be thrown behind a pusher-plate mounted on the bottom of a spacecraft and exploded. The shock wave and radiation from the detonation would impact against the underside of the pusher plate, giving it a powerful push. The pusher plate would be mounted on large two-stage shock absorbers that would smoothly transmit acceleration to the rest of the spacecraft.

During take-off, there were concerns of danger from fluidic shrapnel being reflected from the ground. One proposed solution was to use a flat plate of conventional explosives spread over the pusher plate, and detonate this to lift the ship from the ground before going nuclear. This would lift the ship far enough into the air that the first focused nuclear blast would not create debris capable of harming the ship.

A design for a pulse unit

A preliminary design for a nuclear pulse unit was produced. It proposed the use of a shaped-charge fusion-boosted fission explosive. The explosive was wrapped in a beryllium oxide channel filler, which was surrounded by a uranium radiation mirror. The mirror and channel filler were open ended, and in this open end a flat plate of tungsten propellant was placed. The whole unit was built into a can with a diameter no larger than 6 inches (150 mm) and weighed just over 300 pounds (140 kg) so it could be handled by machinery scaled-up from a soft-drink vending machine; Coca-Cola was consulted on the design.

At 1 microsecond after ignition the gamma bomb plasma and neutrons would heat the channel filler and be somewhat contained by the uranium shell. At 2–3 microseconds the channel filler would transmit some of the energy to the propellant, which vaporized. The flat plate of propellant formed a cigar-shaped explosion aimed at the pusher plate.

The plasma would cool to 25,200 °F (14,000 °C) as it traversed the 82 feet (25 m) distance to the pusher plate and then reheat to 120,600 °F (67,000 °C) as, at about 300 microseconds, it hits the pusher plate and is recompressed. This temperature emits ultraviolet light, which is poorly transmitted through most plasmas. This helps keep the pusher plate cool. The cigar shaped distribution profile and low density of the plasma reduces the instantaneous shock to the pusher plate.

Because the momentum transferred by the plasma is greatest in the center, the pusher plate's thickness would decrease by approximately a factor of 6 from the center to the edge. This ensures the change in velocity is the same for the inner and outer parts of the plate.

At low altitudes where the surrounding air is dense gamma scattering could potentially harm the crew without a radiation shield, a radiation refuge would also be necessary on long missions to survive solar flares. Radiation shielding effectiveness increases exponentially with shield thickness, see gamma ray for a discussion of shielding. On ships with a mass greater than 2,200,000 pounds (1,000,000 kg) the structural bulk of the ship, its stores along with the mass of the bombs and propellant, would provide more than adequate shielding for the crew. Stability was initially thought to be a problem due to inaccuracies in the placement of the bombs, but it was later shown that the effects would cancel out.

Numerous model flight tests, using conventional explosives, were conducted at Point Loma, San Diego in 1959. On November 14, 1959 the one-meter model, also known as "Hot Rod" and "putt-putt", first flew using RDX (chemical explosives) in a controlled flight for 23 seconds to a height of 184 feet (56 m). Film of the tests has been transcribed to video and were featured on the BBC TV program "To Mars by A-Bomb" in 2003 with comments by Freeman Dyson and Arthur C. Clarke. The model landed by parachute undamaged and is in the collection of the Smithsonian National Air and Space Museum.

The first proposed shock absorber was a ring-shaped airbag. It was soon realized that, should an explosion fail, the 1,100,000–2,200,000-pound (500,000–1,000,000 kg) pusher plate would tear away the airbag on the rebound. So a two-stage detuned spring and piston shock absorber design was developed. On the reference design the first stage mechanical absorber was tuned to 4.5 times the pulse frequency whilst the second stage gas piston was tuned to 0.5 times the pulse frequency. This permitted timing tolerances of 10 ms in each explosion.

The final design coped with bomb failure by overshooting and rebounding into a center position. Thus following a failure and on initial ground launch it would be necessary to start or restart the sequence with a lower yield device. In the 1950s methods of adjusting bomb yield were in their infancy and considerable thought was given to providing a means of swapping out a standard yield bomb for a smaller yield one in a 2 or 3 second time frame or to provide an alternative means of firing low yield bombs. Modern variable yield devices would allow a single standardized explosive to be tuned down, configured to a lower yield, automatically.

The bombs had to be launched behind the pusher plate with enough velocity to explode 66–98 feet (20–30 m) beyond it every 1.1 seconds. Numerous proposals were investigated, from multiple guns poking over the edge of the pusher plate to rocket propelled bombs launched from roller coaster tracks, however the final reference design used a simple gas gun to shoot the devices through a hole in the center of the pusher plate.

Potential problems

Exposure to repeated nuclear blasts raises the problem of ablation (erosion) of the pusher plate. Calculations and experiments indicated that a steel pusher plate would ablate less than 1 mm, if unprotected. If sprayed with an oil it would not ablate at all (this was discovered by accident; a test plate had oily fingerprints on it and the fingerprints suffered no ablation). The absorption spectra of carbon and hydrogen minimize heating. The design temperature of the shockwave, 120,600 °F (67,000 °C), emits ultraviolet light. Most materials and elements are opaque to ultraviolet, especially at the 49,000 psi (340 MPa) pressures the plate experiences. This prevents the plate from melting or ablating.

One issue that remained unresolved at the conclusion of the project was whether or not the turbulence created by the combination of the propellant and ablated pusher plate would dramatically increase the total ablation of the pusher plate. According to Freeman Dyson, in the 1960s they would have had to actually perform a test with a real nuclear explosive to determine this; with modern simulation technology this could be determined fairly accurately without such empirical investigation.

Another potential problem with the pusher plate is that of spalling—shards of metal—potentially flying off the top of the plate. The shockwave from the impacting plasma on the bottom of the plate passes through the plate and reaches the top surface. At that point, spalling may occur, damaging the pusher plate. For that reason, alternative substances—plywood and fiberglass—were investigated for the surface layer of the pusher plate and thought to be acceptable.

If the conventional explosives in the nuclear bomb detonate but a nuclear explosion does not ignite, shrapnel could strike and potentially critically damage the pusher plate.

True engineering tests of the vehicle systems were thought to be impossible because several thousand nuclear explosions could not be performed in any one place. Experiments were designed to test pusher plates in nuclear fireballs and long-term tests of pusher plates could occur in space. The shock-absorber designs could be tested at full-scale on Earth using chemical explosives.

However, the main unsolved problem for a launch from the surface of the Earth was thought to be nuclear fallout. Freeman Dyson, group leader on the project, estimated back in the 1960s that with conventional nuclear weapons, each launch would statistically cause on average between 0.1 and 1 fatal cancers from the fallout. That estimate is based on no-threshold model assumptions, a method often used in estimates of statistical deaths from other industrial activities. Each few million dollars of efficiency indirectly gained or lost in the world economy may statistically average lives saved or lost, in terms of opportunity gains versus costs. Indirect effects could matter for whether the overall influence of an Orion-based space program on future human global mortality would be a net increase or a net decrease, including if change in launch costs and capabilities affected space exploration, space colonization, the odds of long-term human species survival, space-based solar power, or other hypotheticals.

Danger to human life was not a reason given for shelving the project. The reasons included lack of a mission requirement, the fact that no one in the U.S. government could think of any reason to put thousands of tons of payload into orbit, the decision to focus on rockets for the Moon mission, and ultimately the signing of the Partial Test Ban Treaty in 1963. The danger to electronic systems on the ground from an electromagnetic pulse was not considered to be significant from the sub-kiloton blasts proposed since solid-state integrated circuits were not in general use at the time.

From many smaller detonations combined, the fallout for the entire launch of a 12,000,000-pound (5,400,000 kg) Orion is equal to the detonation of a typical 10 megaton (40 petajoule) nuclear weapon as an air burst, therefore most of its fallout would be the comparatively dilute delayed fallout. Assuming the use of nuclear explosives with a high portion of total yield from fission, it would produce a combined fallout total similar to the surface burst yield of the Mike shot of Operation Ivy, a 10.4 Megaton device detonated in 1952. The comparison is not quite perfect as, due to its surface burst location, Ivy Mike created a large amount of early fallout contamination. Historical above-ground nuclear weapon tests included 189 megatons of fission yield and caused average global radiation exposure per person peaking at 1.0×10⁻⁵ rem/sq ft (0.11 mSv/a) in 1963, with a 6.5×10⁻⁷ rem/sq ft (0.007 mSv/a) residual in modern times, superimposed upon other sources of exposure, primarily natural background radiation, which averages 0.00022 rem/sq ft (2.4 mSv/a) globally but varies greatly, such as 0.00056 rem/sq ft (6 mSv/a) in some high-altitude cities. Any comparison would be influenced by how population dosage is affected by detonation locations, with very remote sites preferred.

With special designs of the nuclear explosive, Ted Taylor estimated that fission product fallout could be reduced tenfold, or even to zero, if a pure fusion explosive could be constructed instead. A 100% pure fusion explosive has yet to be successfully developed, according to declassified US government documents, although relatively clean PNEs (Peaceful nuclear explosions) were tested for canal excavation by the Soviet Union in the 1970s with 98% fusion yield in the Taiga test's 15 kiloton devices, 0.3 kilotons fission, which excavated part of the proposed Pechora–Kama Canal.

The vehicle's propulsion system and its test program would violate the Partial Test Ban Treaty of 1963, as currently written, which prohibits all nuclear detonations except those conducted underground as an attempt to slow the arms race and to limit the amount of radiation in the atmosphere caused by nuclear detonations. There was an effort by the US government to put an exception into the 1963 treaty to allow for the use of nuclear propulsion for spaceflight but Soviet fears about military applications kept the exception out of the treaty. This limitation would affect only the US, Russia, and the United Kingdom. It would also violate the Comprehensive Nuclear-Test-Ban Treaty which has been signed by the United States and China as well as the de facto moratorium on nuclear testing that the declared nuclear powers have imposed since the 1990s.

The launch of such an Orion nuclear bomb rocket from the ground or low Earth orbit would generate an electromagnetic pulse that could cause significant damage to computers and satellites as well as flooding the van Allen belts with high-energy radiation. Since the EMP footprint would be a few hundred miles wide, this problem might be solved by launching from very remote areas. A few relatively small space-based electrodynamic tethers could be deployed to quickly eject the energetic particles from the capture angles of the Van Allen belts.

An Orion spacecraft could be boosted by non-nuclear means to a safer distance only activating its drive well away from Earth and its satellites. The Lofstrom launch loop or a space elevator hypothetically provide excellent solutions; in the case of the space elevator, existing carbon nanotubes composites, with the possible exception of Colossal carbon tubes, do not yet have sufficient tensile strength. All chemical rocket designs are extremely inefficient and expensive when launching large mass into orbit but could be employed if the result were cost effective.

Notable personnel

• Lew Allen, Contract Manager
• Jerry Astl, explosives engineer
• Jeremy Bernstein, physicist
• Ed Creutz, physicist
• Brian Dunne, Orion's chief scientist
• Freeman Dyson, physicist
• Harry Finger, physicist
• Burt Freeman, physicist
• Harris Mayer, physicist
• James Nance, Project Director
• H. Pierre Noyes, physicist
• Kedar "Bud" Pyatt, mathematician
• Morris Scharff, physicist
• Charles Clark Loomis, physicist
• Ted Taylor, Project Director
• Stanislaw Ulam, mathematician
• Micheal Treshow, physicist
• Ron F. Prater, USAF Liaison
• Edward B. Giller, USAF Liaison
• Don Prickett, USAF Liaison
• Howard R. Kratz, physicist
• Carlo Riparbelli, physicist
• Thomas Macken, physicist
• David Weiss, test pilot
• Rudy A. Cesena, physicist
• Ed A. Day, physicist
• Mike R. Ames, physicist
• Richard D. Morton, physicist
• Reed Watson, physicist
• Richard Goddard, physicist
• Menley Young, physicist
• Michael J. Feeney, physicist
• Jim W. Morris, physicist
• R. N. House, physicist
• Leon Dial, physicist
• W. B. McKinney, physicist
• J. R. Pope, physicist
• Fred W. Ross, physicist
• Perry B Ritter, physicist
• Walt England, physicist
• William(Bill) G. Vulliet, physicist
• John Illes, security guard
• Lois Illes, secretary
• Jonnie Stahl, secretary
• Don Mixson, USAF Liaison
• Robert B Duffield, Chemist
• John J Dishuck, USAF Liaison
• Fred Gorschboth, USAF Liaison
• Ralph Stahl, physicist

Criticism

Professor Glenn Reynolds has written that a less-developed country could leapfrog all others in space by building a massive Orion launcher using 1960's technology.

Operation Plumbbob

Main article: Operation Plumbbob

A test that was similar to the test of a pusher plate occurred as an accidental side effect of a nuclear containment test called "Pascal-B" conducted on 27 August 1957. The test's experimental designer Dr. Robert Brownlee performed a highly approximate calculation that suggested that the low-yield nuclear explosive would accelerate the massive (900 kg) steel capping plate to six times escape velocity. The plate was never found but Dr. Brownlee believes that the plate never left the atmosphere; for example, it could have been vaporized by compression heating of the atmosphere due to its high speed. The calculated velocity was interesting enough that the crew trained a high-speed camera on the plate which, unfortunately, only appeared in one frame indicating a very high lower bound for the speed of the plate.

Notable appearances in fiction

Main article: List of stories featuring nuclear pulse propulsion

The first appearance of the idea in print appears to be Robert A. Heinlein's 1940 short story, "Blowups Happen."

As discussed by Arthur C. Clarke in his recollections of the making of 2001: A Space Odyssey in The Lost Worlds of 2001, a nuclear-pulse version of the U.S. interplanetary spacecraft Discovery One was considered. However the Discovery in the movie did not use this idea, as Stanley Kubrick thought it might be considered parody after making Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb.

An Orion spaceship features prominently in the science fiction novel Footfall by Larry Niven and Jerry Pournelle. In the face of an alien siege/invasion of Earth, the humans must resort to drastic measures to get a fighting ship into orbit to face the alien fleet.

The opening premise of the show Ascension is that in 1963 President John F. Kennedy and the U.S. government, fearing the Cold War will escalate and lead to the destruction of Earth, launched the Ascension, an Orion-class spaceship, to colonize a planet orbiting Proxima Centauri, assuring the survival of the human race.

Author Stephen Baxter's science fiction novel Ark employs an Orion-class generation ship to escape ecological disaster on Earth.

Towards the conclusion of his Empire Games trilogy, Charles Stross includes a spacecraft modeled after Project Orion. The crafts' designers, constrained by a 1960's level of industrial capacity, intend it to be used to explore parallel worlds and to act as a nuclear deterrent, leapfrogging their foes more contemporary capabilities.