Clausius–Clapeyron relation

From Wikipedia, the free encyclopedia

The Clausius–Clapeyron relation, named after Rudolf Clausius^[1] and Benoît Paul Émile Clapeyron,^[2] is a way of characterizing a discontinuous phase transition between two phases of matter of a single constituent. On a pressure–temperature (P–T) diagram, the line separating the two phases is known as the coexistence curve. The Clausius–Clapeyron relation gives the slope of the tangents to this curve. Mathematically,

${\displaystyle {\frac {\mathrm {d} P}{\mathrm {d} T}}={\frac {L}{T\,\Delta v}}={\frac {\Delta s}{\Delta v}},}$

where ${\displaystyle \mathrm {d} P/\mathrm {d} T}$ is the slope of the tangent to the coexistence curve at any point, ${\displaystyle L}$ is the specific latent heat, ${\displaystyle T}$ is the temperature, ${\displaystyle \Delta v}$ is the specific volume change of the phase transition, and ${\displaystyle \Delta s}$ is the specific entropy change of the phase transition.

Derivations

A typical phase diagram. The dotted green line gives the anomalous behavior of water. The Clausius–Clapeyron relation can be used to find the relationship between pressure and temperature along phase boundaries.

Derivation from state postulate

Using the state postulate, take the specific entropy ${\displaystyle s}$ for a homogeneous substance to be a function of specific volume ${\displaystyle v}$ and temperature ${\displaystyle T}$.^[3]:508

${\displaystyle \mathrm {d} s=\left({\frac {\partial s}{\partial v}}\right)_{T}\mathrm {d} v+\left({\frac {\partial s}{\partial T}}\right)_{v}\mathrm {d} T.}$

The Clausius–Clapeyron relation characterizes behavior of a closed system during a phase change, during which temperature and pressure are constant by definition. Therefore,^[3]:508

${\displaystyle \mathrm {d} s=\left({\frac {\partial s}{\partial v}}\right)_{T}\mathrm {d} v.}$

Using the appropriate Maxwell relation gives^[3]:508

${\displaystyle \mathrm {d} s=\left({\frac {\partial P}{\partial T}}\right)_{v}\mathrm {d} v}$

where ${\displaystyle P}$ is the pressure. Since pressure and temperature are constant, by definition the derivative of pressure with respect to temperature does not change.^{[4][5]:57, 62 & 671} Therefore, the partial derivative of specific entropy may be changed into a total derivative

${\displaystyle {\mathrm {d} s}={\frac {\mathrm {d} P}{\mathrm {d} T}}{\mathrm {d} v}}$

and the total derivative of pressure with respect to temperature may be factored out when integrating from an initial phase ${\displaystyle \alpha }$ to a final phase ${\displaystyle \beta }$,^[3]:508 to obtain

${\displaystyle {\frac {\mathrm {d} P}{\mathrm {d} T}}={\frac {\Delta s}{\Delta v}}}$

where ${\displaystyle \Delta s\equiv s_{\beta }-s_{\alpha }}$ and ${\displaystyle \Delta v\equiv v_{\beta }-v_{\alpha }}$ are respectively the change in specific entropy and specific volume. Given that a phase change is an internally reversible process, and that our system is closed, the first law of thermodynamics holds

${\displaystyle \mathrm {d} u=\delta q+\delta w=T\;\mathrm {d} s-P\;\mathrm {d} v}$

where ${\displaystyle u}$ is the internal energy of the system. Given constant pressure and temperature (during a phase change) and the definition of specific enthalpy ${\displaystyle h}$, we obtain

${\displaystyle \mathrm {d} h=\mathrm {d} u+P\;\mathrm {d} v}$

${\displaystyle \mathrm {d} h=T\;\mathrm {d} s}$

${\displaystyle \mathrm {d} s={\frac {\mathrm {d} h}{T}}}$

Given constant pressure and temperature (during a phase change), we obtain^[3]:508

${\displaystyle \Delta s={\frac {\Delta h}{T}}}$

Substituting the definition of specific latent heat ${\displaystyle L=\Delta h}$ gives

${\displaystyle \Delta s={\frac {L}{T}}}$

Substituting this result into the pressure derivative given above (${\displaystyle \mathrm {d} P/\mathrm {d} T=\mathrm {\Delta s} /\mathrm {\Delta v} }$), we obtain^[3]:508[6]

${\displaystyle {\frac {\mathrm {d} P}{\mathrm {d} T}}={\frac {L}{T\Delta v}}.}$

This result (also known as the Clapeyron equation) equates the slope of the tangent to the coexistence curve ${\displaystyle \mathrm {d} P/\mathrm {d} T}$, at any given point on the curve, to the function ${\displaystyle {L}/{T{\Delta v}}}$ of the specific latent heat ${\displaystyle L}$, the temperature ${\displaystyle T}$, and the change in specific volume ${\displaystyle \Delta v}$.

Derivation from Gibbs–Duhem relation

Suppose two phases, ${\displaystyle \alpha }$ and ${\displaystyle \beta }$, are in contact and at equilibrium with each other. Their chemical potentials are related by

${\displaystyle \mu _{\alpha }=\mu _{\beta }.}$

Furthermore, along the coexistence curve,

${\displaystyle \mathrm {d} \mu _{\alpha }=\mathrm {d} \mu _{\beta }.}$

One may therefore use the Gibbs–Duhem relation

${\displaystyle \mathrm {d} \mu =M(-s\mathrm {d} T+v\mathrm {d} P)}$

(where ${\displaystyle s}$ is the specific entropy, ${\displaystyle v}$ is the specific volume, and ${\displaystyle M}$ is the molar mass) to obtain

${\displaystyle -(s_{\beta }-s_{\alpha })\mathrm {d} T+(v_{\beta }-v_{\alpha })\mathrm {d} P=0}$

Rearrangement gives

${\displaystyle {\frac {\mathrm {d} P}{\mathrm {d} T}}={\frac {s_{\beta }-s_{\alpha }}{v_{\beta }-v_{\alpha }}}={\frac {\Delta s}{\Delta v}}}$

from which the derivation of the Clapeyron equation continues as in the previous section.

Ideal gas approximation at low temperatures

When the phase transition of a substance is between a gas phase and a condensed phase (liquid or solid), and occurs at temperatures much lower than the critical temperature of that substance, the specific volume of the gas phase ${\displaystyle v_{\mathrm {g} }}$ greatly exceeds that of the condensed phase ${\displaystyle v_{\mathrm {c} }}$. Therefore, one may approximate

${\displaystyle \Delta v=v_{\mathrm {g} }\left(1-{\tfrac {v_{\mathrm {c} }}{v_{\mathrm {g} }}}\right)\approx v_{\mathrm {g} }}$

at low temperatures. If pressure is also low, the gas may be approximated by the ideal gas law, so that

${\displaystyle v_{\mathrm {g} }=RT/P}$

where ${\displaystyle P}$ is the pressure, ${\displaystyle R}$ is the specific gas constant, and ${\displaystyle T}$ is the temperature. Substituting into the Clapeyron equation

${\displaystyle {\frac {\mathrm {d} P}{\mathrm {d} T}}={\frac {\Delta s}{\Delta v}}}$

we can obtain the Clausius–Clapeyron equation^[3]:509

${\displaystyle {\frac {\mathrm {d} P}{\mathrm {d} T}}={\frac {PL}{T^{2}R}}}$

for low temperatures and pressures,^[3]:509 where ${\displaystyle L}$ is the specific latent heat of the substance.
Let ${\displaystyle (P_{1},T_{1})}$ and ${\displaystyle (P_{2},T_{2})}$ be any two points along the coexistence curve between two phases ${\displaystyle \alpha }$ and ${\displaystyle \beta }$. In general, ${\displaystyle L}$ varies between any two such points, as a function of temperature. But if ${\displaystyle L}$ is constant,

${\displaystyle {\frac {\mathrm {d} P}{P}}={\frac {L}{R}}{\frac {\mathrm {d} T}{T^{2}}},}$

${\displaystyle \int _{P_{1}}^{P_{2}}{\frac {\mathrm {d} P}{P}}={\frac {L}{R}}\int _{T_{1}}^{T_{2}}{\frac {\mathrm {d} T}{T^{2}}}}$

${\displaystyle \left.\ln P\right|_{P=P_{1}}^{P_{2}}=-{\frac {L}{R}}\cdot \left.{\frac {1}{T}}\right|_{T=T_{1}}^{T_{2}}}$

or^[5]:672

${\displaystyle \ln {\frac {P_{1}}{P_{2}}}=-{\frac {L}{R}}\left({\frac {1}{T_{1}}}-{\frac {1}{T_{2}}}\right)}$

These last equations are useful because they relate equilibrium or saturation vapor pressure and temperature to the latent heat of the phase change, without requiring specific volume data.

Applications

Chemistry and chemical engineering

For transitions between a gas and a condensed phase with the approximations described above, the expression may be rewritten as

${\displaystyle \ln P=-{\frac {L}{R}}\left({\frac {1}{T}}\right)+c}$

where ${\displaystyle c}$ is a constant. For a liquid-gas transition, ${\displaystyle L}$ is the specific latent heat (or specific enthalpy) of vaporization; for a solid-gas transition, ${\displaystyle L}$ is the specific latent heat of sublimation. If the latent heat is known, then knowledge of one point on the coexistence curve determines the rest of the curve. Conversely, the relationship between ${\displaystyle \ln P}$ and ${\displaystyle 1/T}$ is linear, and so linear regression is used to estimate the latent heat.

Meteorology and climatology

Atmospheric water vapor drives many important meteorologic phenomena (notably precipitation), motivating interest in its dynamics. The Clausius–Clapeyron equation for water vapor under typical atmospheric conditions (near standard temperature and pressure) is

${\displaystyle {\frac {\mathrm {d} e_{s}}{\mathrm {d} T}}={\frac {L_{v}(T)e_{s}}{R_{v}T^{2}}}}$

where:

• ${\displaystyle e_{s}}$ is saturation vapor pressure
• ${\displaystyle T}$ is temperature
• ${\displaystyle L_{v}}$ is the specific latent heat of evaporation of water
• ${\displaystyle R_{v}}$ is the gas constant of water vapor

The temperature dependence of the latent heat ${\displaystyle L_{v}(T)}$, and therefore of the saturation vapor pressure ${\displaystyle e_{s}(T)}$, cannot be neglected in this application. Fortunately, the August-Roche-Magnus formula provides a very good approximation, using pressure in hPa and temperature in Celsius:

${\displaystyle e_{s}(T)=6.1094\exp \left({\frac {17.625T}{T+243.04}}\right)}$ ^[7][8]

(This is also sometimes called the Magnus or Magnus-Tetens approximation, though this attribution is historically inaccurate.^[9])

Under typical atmospheric conditions, the denominator of the exponent depends weakly on ${\displaystyle T}$ (for which the unit is Celsius). Therefore, the August-Roche-Magnus equation implies that saturation water vapor pressure changes approximately exponentially with temperature under typical atmospheric conditions, and hence the water-holding capacity of the atmosphere increases by about 7% for every 1 °C rise in temperature.^[10]

Example

One of the uses of this equation is to determine if a phase transition will occur in a given situation. Consider the question of how much pressure is needed to melt ice at a temperature ${\displaystyle {\Delta T}}$ below 0 °C. Note that water is unusual in that its change in volume upon melting is negative. We can assume

${\displaystyle {\Delta P}={\frac {L}{T\,\Delta v}}{\Delta T}}$

and substituting in

${\displaystyle L}$ = 3.34×10⁵ J/kg (latent heat of fusion for water),

${\displaystyle T}$ = 273 K (absolute temperature), and

${\displaystyle \Delta v}$ = −9.05×10⁻⁵ m³/kg (change in specific volume from solid to liquid),

we obtain

${\displaystyle {\frac {\Delta P}{\Delta T}}}$ = −13.5 MPa/K.

To provide a rough example of how much pressure this is, to melt ice at −7 °C (the temperature many ice skating rinks are set at) would require balancing a small car (mass = 1000 kg^[11]) on a thimble (area = 1 cm²).

Second derivative

While the Clausius–Clapeyron relation gives the slope of the coexistence curve, it does not provide any information about its curvature or second derivative. The second derivative of the coexistence curve of phases 1 and 2 is given by ^[12]

${\displaystyle {\begin{aligned}{\frac {\mathrm {d} ^{2}P}{\mathrm {d} T^{2}}}={\frac {1}{v_{2}-v_{1}}}\left[{\frac {c_{p2}-c_{p1}}{T}}-2(v_{2}\alpha _{2}-v_{1}\alpha _{1}){\frac {\mathrm {d} P}{\mathrm {d} T}}\right]+\\{\frac {1}{v_{2}-v_{1}}}\left[(v_{2}\kappa _{T2}-v_{1}\kappa _{T1})\left({\frac {\mathrm {d} P}{\mathrm {d} T}}\right)^{2}\right],\end{aligned}}}$

where subscripts 1 and 2 denote the different phases, ${\displaystyle c_{p}}$ is the specific heat capacity at constant pressure, ${\displaystyle \alpha =(1/v)(\mathrm {d} v/\mathrm {d} T)_{P}}$ is the thermal expansion coefficient, and ${\displaystyle \kappa _{T}=-(1/v)(\mathrm {d} v/\mathrm {d} P)_{T}}$ is the isothermal compressibility.

Solar wind

From Wikipedia, the free encyclopedia

Ulysses observations of solar wind speed as a function of helio latitude during solar minimum. Slow wind (~400 km/s) is confined to the equatorial regions, while fast wind (~750 km/s) is seen over the poles.^[1] Red/blue colours show inward/outward polarities of the heliospheric magnetic field.

The solar wind is a stream of charged particles released from the upper atmosphere of the Sun. This plasma consists of mostly electrons, protons and alpha particles with thermal energies between 1.5 and 10 keV. Embedded within the solar-wind plasma is the interplanetary magnetic field.^[2] The solar wind varies in density, temperature and speed over time and over solar latitude and longitude. Its particles can escape the Sun's gravity because of their high energy resulting from the high temperature of the corona, which in turn is a result of the coronal magnetic field.

At a distance of more than a few solar radii from the sun, the solar wind is supersonic and reaches speeds of 250 to 750 kilometers per second.^[3] The flow of the solar wind is no longer supersonic at the termination shock. The Voyager 2 spacecraft crossed the shock more than five times between 30 August and 10 December 2007.^[4] Voyager 2 crossed the shock about a billion kilometers closer to the Sun than the 13.5 billion kilometer distance where Voyager 1 came upon the termination shock.^[5][6] The spacecraft moved outward through the termination shock into the heliosheath and onward toward the interstellar medium. Other related phenomena include the aurora (northern and southern lights), the plasma tails of comets that always point away from the Sun, and geomagnetic storms that can change the direction of magnetic field lines.

History

The existence of particles flowing outward from the Sun to the Earth was first suggested by British astronomer Richard C. Carrington. In 1859, Carrington and Richard Hodgson independently made the first observation of what would later be called a solar flare. This is a sudden, localised increase in brightness on the solar disc, which is now known^[7] to often occur in conjunction with an episodic ejection of material and magnetic flux from the Sun's atmosphere, known as a coronal mass ejection. On the following day, a geomagnetic storm was observed, and Carrington suspected that there might be a connection, which is now attributed to the arrival of the coronal mass ejection in near-Earth space and its subsequent interaction with the Earth's magnetosphere. George FitzGerald later suggested that matter was being regularly accelerated away from the Sun and was reaching the Earth after several days.^[8]

Laboratory simulation of the magnetosphere's influence on the Solar Wind; these auroral-like Birkeland currents were created in a terrella, a magnetised anode globe in an evacuated chamber.

In 1910 British astrophysicist Arthur Eddington essentially suggested the existence of the solar wind, without naming it, in a footnote to an article on Comet Morehouse.^[9] The idea never fully caught on even though Eddington had also made a similar suggestion at a Royal Institution address the previous year. In the latter case, he postulated that the ejected material consisted of electrons while in his study of Comet Morehouse he supposed them to be ions.^[9]

The first person to suggest that the ejected material consisted of both ions and electrons was Kristian 
Birkeland. His geomagnetic surveys showed that auroral activity was nearly uninterrupted. As these displays and other geomagnetic activity were being produced by particles from the Sun, he concluded that the Earth was being continually bombarded by "rays of electric corpuscles emitted by the Sun".^[8] In 1916, Birkeland proposed that, "From a physical point of view it is most probable that solar rays are neither exclusively negative nor positive rays, but of both kinds". In other words, the solar wind consists of both negative electrons and positive ions.^[10] Three years later in 1919, Frederick Lindemann also suggested that particles of both polarities, protons as well as electrons, come from the Sun.^[11]

Around the 1930s, scientists had determined that the temperature of the solar corona must be a million degrees Celsius because of the way it stood out into space (as seen during total eclipses). Later spectroscopic work confirmed this extraordinary temperature. In the mid-1950s Sydney Chapman calculated the properties of a gas at such a temperature and determined it was such a superb conductor of heat that it must extend way out into space, beyond the orbit of Earth. Also in the 1950s, Ludwig Biermann became interested in the fact that no matter whether a comet is headed towards or away from the Sun, its tail always points away from the Sun. Biermann postulated that this happens because the Sun emits a steady stream of particles that pushes the comet's tail away.^[12] Wilfried Schröder claimed that Paul Ahnert was the first to relate solar wind to comet tail direction based on observations of the comet Whipple-Fedke (1942g).^[13]

Eugene Parker realised that the heat flowing from the Sun in Chapman's model and the comet tail blowing away from the Sun in Biermann's hypothesis had to be the result of the same phenomenon, which he termed the "solar wind".^[14][15] Parker showed in 1958 that even though the Sun's corona is strongly attracted by solar gravity, it is such a good heat conductor that it is still very hot at large distances. Since gravity weakens as distance from the Sun increases, the outer coronal atmosphere escapes supersonically into interstellar space. Furthermore, Parker was the first person to notice that the weakening effect of the gravity has the same effect on hydrodynamic flow as a de Laval nozzle: it incites a transition from subsonic to supersonic flow.^[16]

Opposition to Parker's hypothesis on the solar wind was strong. The paper he submitted to the Astrophysical Journal in 1958 was rejected by two reviewers. It was saved by the editor Subrahmanyan Chandrasekhar (who later received the 1983 Nobel Prize in physics).

In January 1959, the Soviet satellite Luna 1 first directly observed the solar wind and measured its strength.^[17][18][19] They were detected by hemispherical ion traps. The discovery, made by Konstantin Gringauz, was verified by Luna 2, Luna 3 and by the more distant measurements of Venera 1. Three years later its measurement was performed by Neugebauer and collaborators using the Mariner 2 spacecraft.^[20]

In the late 1990s the Ultraviolet Coronal Spectrometer (UVCS) instrument on board the SOHO spacecraft observed the acceleration region of the fast solar wind emanating from the poles of the Sun and found that the wind accelerates much faster than can be accounted for by thermodynamic expansion alone. Parker's model predicted that the wind should make the transition to supersonic flow at an altitude of about 4 solar radii from the photosphere (surface); but the transition (or "sonic point") now appears to be much lower, perhaps only 1 solar radius above the photosphere, suggesting that some additional mechanism accelerates the solar wind away from the Sun. The acceleration of the fast wind is still not understood and cannot be fully explained by Parker's theory. The gravitational and electromagnetic explanation for this acceleration is, however, detailed in an earlier paper by 1970 Nobel laureate for Physics, Hannes Alfvén.^[21][22]

The first numerical simulation of the solar wind in the solar corona including closed and open field lines was performed by Pneuman and Kopp in 1971. The magnetohydrodynamics equations in steady state were solved iteratively starting with an initial dipolar configuration.^[23]

In 1990, the Ulysses probe was launched to study the solar wind from high solar latitudes. All prior observations had been made at or near the Solar System's ecliptic plane.^[24]

Acceleration

While early models of the solar wind relied primarily on thermal energy to accelerate the material, by the 1960s it was clear that thermal acceleration alone cannot account for the high speed of solar wind. An additional unknown acceleration mechanism is required and likely relates to magnetic fields in the solar atmosphere.

The Sun's corona, or extended outer layer, is a region of plasma that is heated to over a million kelvin. As a result of thermal collisions, the particles within the inner corona have a range and distribution of speeds described by a Maxwellian distribution. The mean velocity of these particles is about 145 km/s, which is well below the solar escape velocity of 618 km/s. However, a few of the particles achieve energies sufficient to reach the terminal velocity of 400 km/s, which allows them to feed the solar wind. At the same temperature, electrons, due to their much smaller mass, reach escape velocity and build up an electric field that further accelerates ions away from the Sun.^[25]

The total number of particles carried away from the Sun by the solar wind is about 1.3×10³⁶ per second.^[26] Thus, the total mass loss each year is about (2–3)×10⁻¹⁴ solar masses,^[27] or about one billion kilograms per second. This is equivalent to losing a mass equal to the Earth every 150 million years.^[28] However, only about 0.01% of the Sun's total mass has been lost through the solar wind.^[29] Other stars have much stronger stellar winds that result in significantly higher mass loss rates.

Properties and structure

Fast and slow solar wind

The solar wind is observed to exist in two fundamental states, termed the slow solar wind and the fast solar wind, though their differences extend well beyond their speeds. In near-Earth space, the slow solar wind is observed to have a velocity of 300–500 km/s, a temperature of 1.4–1.6×10⁶ K and a composition that is a close match to the corona. By contrast, the fast solar wind has a typical velocity of 750 km/s, a temperature of 8×10⁵ K and it nearly matches the composition of the Sun's photosphere.^[30] The slow solar wind is twice as dense and more variable in nature than the fast solar wind.^[26][31]

The slow solar wind appears to originate from a region around the Sun's equatorial belt that is known as the "streamer belt", where coronal streamers are produced by magnetic flux open to the heliosphere draping over closed magnetic loops. The exact coronal structures involved in slow solar wind formation and the method by which the material is released is still under debate.^[32][33][34] Observations of the Sun between 1996 and 2001 showed that emission of the slow solar wind occurred at latitudes up to 30–35° during the solar minimum (the period of lowest solar activity), then expanded toward the poles as the solar cycle approached maximum. At solar maximum, the poles were also emitting a slow solar wind.^[1]

The fast solar wind originates from coronal holes,^[35] which are funnel-like regions of open field lines in the Sun's magnetic field.^[36] Such open lines are particularly prevalent around the Sun's magnetic poles. The plasma source is small magnetic fields created by convection cells in the solar atmosphere. These fields confine the plasma and transport it into the narrow necks of the coronal funnels, which are located only 20,000 kilometers above the photosphere. The plasma is released into the funnel when these magnetic field lines reconnect.^[37]

Pressure

The wind exerts a pressure at 1 AU typically in the range of 1–6 nPa (1–6×10⁻⁹ N/m²), although it can readily vary outside that range.

The dynamic pressure is a function of wind speed and density. The formula is
P = 1.6726×10⁻⁶ * n * V²
where pressure P is in nPa (nanopascals), n is the density in particles/cm³ and V is the speed in km/s of the solar wind.^[38]

Coronal mass ejection

Both the fast and slow solar wind can be interrupted by large, fast-moving bursts of plasma called interplanetary coronal mass ejections, or ICMEs. ICMEs are the interplanetary manifestation of solar coronal mass ejections, which are caused by release of magnetic energy at the Sun. CMEs are often called "solar storms" or "space storms" in the popular media. They are sometimes, but not always, associated with solar flares, which are another manifestation of magnetic energy release at the Sun. ICMEs cause shock waves in the thin plasma of the heliosphere, launching electromagnetic waves and accelerating particles (mostly protons and electrons) to form showers of ionizing radiation that precede the CME.
When a CME impacts the Earth's magnetosphere, it temporarily deforms the Earth's magnetic field, changing the direction of compass needles and inducing large electrical ground currents in Earth itself; this is called a geomagnetic storm and it is a global phenomenon. CME impacts can induce magnetic reconnection in Earth's magnetotail (the midnight side of the magnetosphere); this launches protons and electrons downward toward Earth's atmosphere, where they form the aurora.

ICMEs are not the only cause of space weather. Different patches on the Sun are known to give rise to slightly different speeds and densities of wind depending on local conditions. In isolation, each of these different wind streams would form a spiral with a slightly different angle, with fast-moving streams moving out more directly and slow-moving streams wrapping more around the Sun. Fast moving streams tend to overtake slower streams that originate westward of them on the Sun, forming turbulent co-rotating interaction regions that give rise to wave motions and accelerated particles, and that affect Earth's magnetosphere in the same way as, but more gently than, CMEs.

Solar System effects

The heliospheric current sheet results from the influence of the Sun's rotating magnetic field on the plasma in the solar wind.

Over the Sun's lifetime, the interaction of its surface layers with the escaping solar wind has significantly decreased its surface rotation rate.^[39] The wind is considered responsible for comets' tails, along with the Sun's radiation.^[40] The solar wind contributes to fluctuations in celestial radio waves observed on the Earth, through an effect called interplanetary scintillation.^[41]

Magnetospheres

Schematic of Earth's magnetosphere. The solar wind flows from left to right.

Where the solar wind intersects with a planet that has a well-developed magnetic field (such as Earth, Jupiter and Saturn), the particles are deflected by the Lorentz force. This region, known as the magnetosphere, causes the particles to travel around the planet rather than bombarding the atmosphere or surface. The magnetosphere is roughly shaped like a hemisphere on the side facing the Sun, then is drawn out in a long wake on the opposite side. The boundary of this region is called the magnetopause, and some of the particles are able to penetrate the magnetosphere through this region by partial reconnection of the magnetic field lines.^[25]

Noon meridian section of magnetosphere.

The solar wind is responsible for the overall shape of Earth's magnetosphere. Fluctuations in its speed, density, direction, and entrained magnetic field strongly affect Earth's local space environment. For example, the levels of ionizing radiation and radio interference can vary by factors of hundreds to thousands; and the shape and location of the magnetopause and bow shock wave upstream of it can change by several Earth radii, exposing geosynchronous satellites to the direct solar wind. These phenomena are collectively called space weather.

From the European Space Agency’s Cluster mission, a new study has taken place that proposes that it is easier for the solar wind to infiltrate the magnetosphere than previously believed. A group of scientists directly observed the existence of certain waves in the solar wind that were not expected. A recent study shows that these waves enable incoming charged particles of solar wind to breach the magnetopause. This suggests that the magnetic bubble forms more as a filter than a continuous barrier. This latest discovery occurred through the distinctive arrangement of the four identical Cluster spacecraft, which fly in a controlled configuration through near-Earth space. As they sweep from the magnetosphere into interplanetary space and back again, the fleet provides exceptional three-dimensional insights on the phenomena that connect the sun to Earth.

The research characterized variances in formation of the interplanetary magnetic field (IMF) largely influenced by Kelvin-Helmholtz waves (which occur at the interface of two fluids) as a result of differences in thickness and numerous other characteristics of the boundary layer. Experts believe that this was the first occasion that the appearance of Kelvin-Helmholtz waves at the magnetopause had been displayed at high latitude dawnward orientation of the IMF. These waves are being seen in unforeseen places under solar wind conditions that were formerly believed to be undesired for their generation. These discoveries show how Earth’s magnetosphere can be penetrated by solar particles under specific IMF circumstances. The findings are also relevant to studies of magnetospheric progressions around other planetary bodies. This study suggests that Kelvin-Helmholtz waves can be a somewhat common, and possibly constant, instrument for the entrance of solar wind into terrestrial magnetospheres under various IMF orientations.^[42]

Atmospheres

The solar wind affects other incoming cosmic rays interacting with planetary atmospheres. Moreover, planets with a weak or non-existent magnetosphere are subject to atmospheric stripping by the solar wind.

Venus, the nearest and most similar planet to Earth, has 100 times denser atmosphere, with little or no geo-magnetic field. Space probes discovered a comet-like tail that extends to Earth's orbit.^[43]

Earth itself is largely protected from the solar wind by its magnetic field, which deflects most of the charged particles; however some of the charged particles are trapped in the Van Allen radiation belt. A smaller number of particles from the solar wind manage to travel, as though on an electromagnetic energy transmission line, to the Earth's upper atmosphere and ionosphere in the auroral zones. The only time the solar wind is observable on the Earth is when it is strong enough to produce phenomena such as the aurora and geomagnetic storms. Bright auroras strongly heat the ionosphere, causing its plasma to expand into the magnetosphere, increasing the size of the plasma geosphere and injecting atmospheric matter into the solar wind. Geomagnetic storms result when the pressure of plasmas contained inside the magnetosphere is sufficiently large to inflate and thereby distort the geomagnetic field.

Although Mars is larger than Mercury and four times farther from the Sun, it is thought that the solar wind has stripped away up to a third of its original atmosphere, leaving a layer 1/100th as dense as the Earth's. It is believed the mechanism for this atmospheric stripping is gas caught in bubbles of magnetic field, which are ripped off by solar winds.^[44] In 2015 the NASA Mars Atmosphere and Volatile Evolution (MAVEN) mission measured the rate of atmospheric stripping caused by the magnetic field carried by the solar wind as it flows past Mars, which generates an electric field, much as a turbine on Earth can be used to generate electricity. This electric field accelerates electrically charged gas atoms, called ions, in Mars’ upper atmosphere and shoots them into space.^[45] The MAVEN mission measured the rate of atmospheric stripping at about 100 grams (~1/4 lb) per second.^[46]

Moons and planetary surfaces

Apollo's SWC experiment

Mercury, the nearest planet to the Sun, bears the full brunt of the solar wind, and since its atmosphere is vestigial and transient, its surface is bathed in radiation.

Mercury has an intrinsic magnetic field, so under normal solar wind conditions, the solar wind cannot penetrate its magnetosphere and particles only reach the surface in the cusp regions. During coronal mass ejections, however, the magnetopause may get pressed into the surface of the planet, and under these conditions, the solar wind may interact freely with the planetary surface.

The Earth's Moon has no atmosphere or intrinsic magnetic field, and consequently its surface is bombarded with the full solar wind. The Project Apollo missions deployed passive aluminum collectors in an attempt to sample the solar wind, and lunar soil returned for study confirmed that the lunar regolith is enriched in atomic nuclei deposited from the solar wind. These elements may prove useful resources for lunar colonies.^[47]

Outer limits

The solar wind "blows a bubble" in the interstellar medium (the rarefied hydrogen and helium gas that permeates the galaxy). The point where the solar wind's strength is no longer great enough to push back the interstellar medium is known as the heliopause and is often considered to be the outer border of the Solar System. The distance to the heliopause is not precisely known and probably depends on the current velocity of the solar wind and the local density of the interstellar medium, but it is far outside Pluto's orbit. Scientists hope to gain perspective on the heliopause from data acquired through the Interstellar Boundary Explorer (IBEX) mission, launched in October 2008.

Notable events

• From May 10 to May 12, 1999, NASA's Advanced Composition Explorer (ACE) and WIND spacecraft observed a 98% decrease of solar wind density. This allowed energetic electrons from the Sun to flow to Earth in narrow beams known as "strahl", which caused a highly unusual "polar rain" event, in which a visible aurora appeared over the North Pole. In addition, Earth's magnetosphere increased to between 5 and 6 times its normal size.^[48]
• On 13 December 2010, Voyager 1 determined that the velocity of the solar wind, at its location 10.8 billion miles from Earth had slowed to zero. "We have gotten to the point where the wind from the Sun, which until now has always had an outward motion, is no longer moving outward; it is only moving sideways so that it can end up going down the tail of the heliosphere, which is a comet-shaped-like object," said Voyager project scientist Edward Stone.^[49][50]

Mars Direct

From Wikipedia, the free encyclopedia

Mars Direct is a proposal for a human mission to Mars which purports to be both cost-effective and possible with current technology. It was originally detailed in a research paper by Martin Marietta engineers Robert Zubrin and David Baker in 1990, and later expanded upon in Zubrin's 1996 book The Case for Mars. It now serves as a staple of Zubrin's speaking engagements and general advocacy as head of the Mars Society, an organization devoted to the colonization of Mars.^[1]

The Habitat Unit and the Earth Return Vehicle on Mars.

History

Space Exploration Initiative

On July 20, 1989, George H. W. Bush – then President of the United States – announced plans for what came to be known as the Space Exploration Initiative (SEI). In a speech on the steps of the National Air and Space Museum he described long-term plans which would culminate in a manned mission to the surface of Mars.^[2]

By December 1990, a study to estimate the project's cost determined that long-term expenditure would total approximately 450 billion dollars spread over 20 to 30 years.^[3] The "90 Day Study" as it came to be known, evoked a hostile Congressional reaction towards SEI given that it would have required the largest single government expenditure since World War II.^[4] Within a year, all funding requests for SEI had been denied.

Dan Goldin became NASA Administrator on April 1, 1992, officially abandoning plans for near-term human exploration beyond Earth orbit with the shift towards a "faster, better, cheaper" strategy for robotic exploration.^[5]

Development

While working at Martin Marietta designing interplanetary mission architectures, Robert Zubrin perceived a fundamental flaw in the SEI program. Zubrin came to understand that if NASA's plan was to fully utilize as many technologies as possible in support of sending the mission to Mars, it would become politically untenable. In his own words:

The exact opposite of the correct way to do engineering.^[4]

Zubrin's alternative to this "Battlestar Galactica" mission strategy (dubbed so by its detractors for the large, nuclear powered spaceships that supposedly resembled the science-fiction spaceship of the same name) involved a longer surface stay, a faster flight-path in the form of a conjunction class mission, in-situ resource utilization and craft launched directly from the surface of Earth to Mars as opposed to be being assembled in orbit or by a space-based drydock.^[6] After receiving approval from management at Marietta, a 12-man team within the company began to work out the details of the mission. While they focused primarily on more traditional mission architectures, Zubrin began to collaborate with colleague David Baker's^[7] extremely simple, stripped-down and robust strategy. Their goal to "use local resources, travel light, and live off the land" became the hallmark of Mars Direct.^[4]

Mission scenario

First launch

The first flight of the Ares rocket (not to be confused with the similarly named rocket of the now defunct Constellation program) would take an unmanned Earth Return Vehicle to Mars after a 6-month cruise phase, with a supply of hydrogen, a chemical plant and a small nuclear reactor. Once there, a series of chemical reactions (the Sabatier reaction coupled with electrolysis) would be used to combine a small amount of hydrogen (8 tons) carried by the Earth Return Vehicle with the carbon dioxide of the Martian atmosphere to create up to 112 tonnes of methane and oxygen. This relatively simple chemical-engineering procedure was used regularly in the 19th and 20th centuries,^[8] and would ensure that only 7% of the return propellant would need to be carried to the surface of Mars.
96 tonnes of methane and oxygen would be needed to send the Earth Return Vehicle on a trajectory back home at the conclusion of the surface stay; the rest would be available for Mars rovers. The process of generating fuel is expected to require approximately ten months to complete.

Second launch

Some 26 months after the Earth Return Vehicle is originally launched from Earth, a second vehicle, the Mars Habitat Unit, would be launched on a 6-month long low-energy transfer trajectory to Mars, and would carry a crew of four astronauts (the minimum number required so that the team can be split in two without leaving anyone alone). The Habitat Unit would not be launched until the automated factory aboard the ERV had signaled the successful production of chemicals required for operation on the planet and the return trip to Earth. During the trip, artificial gravity would be generated by tethering the Habitat Unit to the spent upper stage of the booster, and setting them rotating about a common axis. This rotation would produce a comfortable 1 g working environment for the astronauts, freeing them of the debilitating effects of long-term exposure to weightlessness.^[4]

Landing and surface operations

Upon reaching Mars, the upper stage would be jettisoned, with the Habitat Unit aerobraking into Mars orbit before soft-landing in proximity to the Earth Return Vehicle. Precise landing would be supported by a radar beacon started by the first lander. Once on Mars, the crew would spend 18 months on the surface, carrying out a range of scientific research, aided by a small rover vehicle carried aboard their Mars Habitat Unit, and powered by the methane produced by the Earth Return Vehicle.

Return and follow-up missions

To return, the crew would use the Earth Return Vehicle, leaving the Mars Habitat Unit for the possible use of subsequent explorers. On the return trip to Earth, the propulsion stage of the Earth Return Vehicle would be used as a counterweight to generate artificial gravity for the trip back.
Follow-up missions would be dispatched at 2 year intervals to Mars to ensure that a redundant ERV would be on the surface at all times, waiting to be used by the next crewed mission or the current crew in an emergency. In such an emergency scenario, the crew would trek hundreds of kilometers to the other ERV in their long-range vehicle.

Components

The Mars Direct proposal includes a component for a Launch Vehicle "Ares", an Earth Return Vehicle (ERV) and a Mars Habitat Unit (MHU).

Launch Vehicle

The plan involves several launches making use of heavy-lift boosters of similar size to the Saturn V used for the Apollo missions, which would potentially be derived from Space Shuttle components. This proposed rocket is dubbed "Ares", which would use space shuttle Advanced Solid Rocket Boosters, a modified shuttle external tank, and a new Lox/LH2 third stage for the trans-Mars injection of the payload. Ares would put 121 tonnes into a 300 km circular orbit, and boost 47 tonnes toward Mars.^[9]

Earth Return Vehicle

The Earth Return Vehicle is a two-stage vehicle. The upper stage comprises the living accommodation for the crew during their six-month return trip to Earth from Mars. The lower stage contains the vehicle's rocket engines and a small chemical production plant.

Mars Habitat Unit

The Mars Habitat Unit is a 2- or 3-deck vehicle providing a comprehensive living and working environment for a Mars crew. In addition to individual sleeping quarters which provide a degree of privacy for each of the crew and a place for personal effects, the Mars Habitat Unit includes a communal living area, a small galley, exercise area, and hygiene facilities with closed-cycle water purification. The lower deck of the Mars Habitat Unit provides the primary working space for the crew: small laboratory areas for carrying out geology and life science research; storage space for samples, airlocks for reaching the surface of Mars, and a suiting-up area where crew members prepare for surface operations. Protection from harmful radiation while in space and on the surface of Mars (e.g. from solar flares) would be provided by a dedicated "storm shelter" in the core of the vehicle.

The Mars Habitat Unit would also include a small pressurized rover that is stored in the lower deck area and assembled on the surface of Mars. Powered by a methane engine, it is designed to extend the range over which astronauts can explore the surface of Mars out to 320 km.

Since it was first proposed as a part of Mars Direct, the Mars Habitat Unit has been adopted by NASA as a part of their Mars Design Reference Mission, which uses two Mars Habitat Units – one of which flies to Mars unmanned, providing a dedicated laboratory facility on Mars, together with the capacity to carry a larger rover vehicle. The second Mars Habitat Unit flies to Mars with the crew, its interior given over completely to living and storage space.

To prove the viability of the Mars Habitat Unit, the Mars Society has implemented the Mars Analogue Research Station Program (MARS), which has established a number of prototype Mars Habitat Units around the world.

Reception

Baker pitched Mars Direct at the Marshall Spaceflight Center in April 1990,^[10] where reception was very positive. The engineers flew around the country to present their plan, which generated significant interest. When their tour culminated in a demonstration at the National Space Society they received a standing ovation.^[4] The plan gained rapid media attention shortly afterwards.

Resistance to the plan came from teams within NASA working on the Space Station and advanced propulsion concepts^{[citation needed]}. The NASA administration rejected Mars Direct. Zubrin remained committed to the strategy, and after parting with David Baker attempted to convince the new NASA administration of Mars Direct's merits in 1992.^[4]

After being granted a small research fund at Martin Marietta, Zubrin and his colleagues successfully demonstrated an in-situ propellant generator which achieved an efficiency of 94%.^[4] No chemical engineers partook in the development of the demonstration hardware.^[4] After showing the positive results to the Johnson Space Center, the NASA administration still held several reservations about the plan.^[4]

In November 2003, Zubrin was invited to speak to the U.S. Senate committee on the future of space exploration.^[4] Two months later the Bush administration announced the creation of the Constellation program, a manned spaceflight initiative with the goal of sending humans to the Moon by 2020. While a Mars mission was not specifically detailed, a plan to reach Mars based on utilizing the Orion spacecraft was tentatively developed for implementation in the 2030s. The program's funding was denied in 2011 by the Obama administration^{[citation needed]} and the Constellation program ended.

There are a variety of psychological and sociological issues affecting long-duration expeditionary space missions. Early human spaceflight missions to Mars are expected to have significant psycho-social problems to overcome, as well as provide considerable data for refining mission design, mission planning, and crew selection for future missions.^[11]

Revisions

Since Mars Direct was initially conceived, it has undergone regular review and development by Zubrin himself, the Mars Society, NASA, Stanford University and others.

Mars Semi-Direct

Artist's rendering of Mars Semi-Direct/DRA 1.0: The Manned Habitat Unit is "docked" alongside a pre placed habitat that was sent ahead of the Earth Return Vehicle.

Zubrin and Weaver developed a modified version of Mars Direct, called Mars Semi-Direct, in response to some specific criticisms.^[12] This mission consists of three spacecraft and includes a "Mars Ascent Vehicle" (MAV). The ERV remains in Mars orbit for the return journey, while the unmanned MAV lands and manufactures propellants for the ascent back up to Mars orbit. The Mars Semi-Direct architecture has been used as the basis of a number of studies, including the NASA Design Reference Missions.

When subjected to the same cost-analysis as the 90-day report, Mars Semi-Direct was predicted to cost 55 billion dollars over 10 years, capable of fitting into the existing NASA budget.

Mars Semi-Direct became the basis of the Design Reference Mission 1.0 of NASA, replacing the 90-day report.

Design Reference Mission

The NASA model, referred to as the Design Reference Mission, on version 5.0 as of September 1, 2012, calls for a significant upgrade in hardware (at least three launches per mission, rather than two), and sends the ERV to Mars fully fueled, parking it in orbit above the planet for subsequent rendezvous with the MAV.

Mars Direct and SpaceX

With the potentially imminent advent of low-cost heavy lift capability, Zubrin has posited a dramatically lower cost manned Mars mission using hardware developed by space transport company SpaceX. In this simpler plan, a crew of two would be sent to Mars by a single Falcon Heavy launch, the Dragon spacecraft acting as their interplanetary cruise habitat. Additional living space for the journey would be enabled through the use of inflatable add-on modules if required. The problems associated with long-term weightlessness would be addressed in the same manner as the baseline Mars Direct plan, a tether between the Dragon habitat and the TMI (Trans-Mars Injection) stage acting to allow rotation of the craft.

The Dragon's heatshield characteristics could allow for a safe descent if landing rockets of sufficient power were made available. Research at NASA's Ames Research Center has demonstrated that a robotic Dragon would be capable of a fully propulsive landing on the Martian surface.^{[citation needed]} On the surface, the crew would have at their disposal two Dragon spacecraft with inflatable modules as habitats, two ERVs, two Mars ascent vehicles and 8 tonnes of cargo.

Other Studies

The Mars Society and Stanford studies retain the original two-vehicle mission profile of Mars Direct, but increase the crew size to six.

Mars Society Australia developed their own four-person Mars Oz reference mission, based on Mars Semi-Direct. This study uses horizontally landing, bent biconic shaped modules, and relies on solar power and chemical propulsion throughout,^[13] where Mars Direct and the DRMs used nuclear reactors for surface power and, in the case of the DRMs for propulsion as well. The Mars Oz reference mission also differs in assuming, based on space station experience, that spin gravity will not be required.

Mars Analogue Research Stations

The Mars Society has argued the viability of the Mars Habitat Unit concept through their Mars Analogue Research Station program. These are two or three decked vertical cylinders ~8 m in diameter and 8 m high. Mars Society Australia plans to build its own station based on the Mars Oz design.^[14] The Mars Oz design features a horizontal cylinder 4.7 m in diameter and 18 m long, with a tapered nose. A second similar module will function as a garage and power and logistics module.
Mars Direct was featured on a Discovery Channel programs Mars: The Next Frontier in which issues were discussed surrounding NASA funding of the project, and on Mars Underground, where the plan is discussed more in-depth.

Alternatives

"Mars to Stay" proposals involve not returning the first immigrant/explorers immediately, or ever. It has been suggested the cost of sending a four or six person team could be one fifth to one tenth the cost of returning that same four or six person team. Depending on the precise approach taken, a quite complete lab could be sent and landed for less than the cost of sending back even 50 kilos of Martian rocks. Twenty or more persons could be sent for the cost of returning four.^[15]

In fiction

• Mars Direct is the mission mode used in Gregory Benford's novel The Martian Race, Geoffrey A. Landis's novel Mars Crossing, Larry Niven's novel Rainbow Mars, Robert M. Blevins' novel The 13th Day of Christmas, as well as Zubrin's own novel, First Landing.
• Mars Direct forms the basis for the 2000 film Mission to Mars.
• In the Futurama episode "The Luck of the Fryrish", a short clip shows the first man on Mars with a spacecraft that resembles the Mars Habitat Unit.
• In the West Wing episode "The Warfare of Genghis Khan", a NASA staffer describes Mars Direct to the skeptical White House Deputy Chief of Staff Josh Lyman and is able to convince him of its merit.
• Both Mars Direct and Mars for Less concepts figure prominently in Brian Enke's 2004 novel, Shadows of Medusa.
• The Martian, a novel by Andy Weir, describes the Ares missions, a series of manned missions to Mars, using Mars Semi-Direct.