Dipole

From Wikipedia, the free encyclopedia

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

The magnetic field of a sphere with a north magnetic pole at the top and a south magnetic pole at the bottom. By comparison, Earth has a south magnetic pole near its north geographic pole and a north magnetic pole near its south pole.

In physics, a dipole (from Greek δίς (dis) 'twice', and πόλος (polos) 'axis') is an electromagnetic phenomenon which occurs in two ways:

• An electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple example of this system is a pair of charges of equal magnitude but opposite sign separated by some typically small distance. (A permanent electric dipole is called an electret.)
• A magnetic dipole is the closed circulation of an electric current system. A simple example is a single loop of wire with constant current through it. A bar magnet is an example of a magnet with a permanent magnetic dipole moment.

Dipoles, whether electric or magnetic, can be characterized by their dipole moment, a vector quantity. For the simple electric dipole, the electric dipole moment points from the negative charge towards the positive charge, and has a magnitude equal to the strength of each charge times the separation between the charges. (To be precise: for the definition of the dipole moment, one should always consider the "dipole limit", where, for example, the distance of the generating charges should converge to 0 while simultaneously, the charge strength should diverge to infinity in such a way that the product remains a positive constant.)

For the magnetic (dipole) current loop, the magnetic dipole moment points through the loop (according to the right hand grip rule), with a magnitude equal to the current in the loop times the area of the loop.

Similar to magnetic current loops, the electron particle and some other fundamental particles have magnetic dipole moments, as an electron generates a magnetic field identical to that generated by a very small current loop. However, an electron's magnetic dipole moment is not due to a current loop, but to an intrinsic property of the electron. The electron may also have an electric dipole moment though such has yet to be observed (see electron electric dipole moment).

Contour plot of the electrostatic potential of a horizontally oriented electrical dipole of infinitesimal size. Strong colors indicate highest and lowest potential (where the opposing charges of the dipole are located).

A permanent magnet, such as a bar magnet, owes its magnetism to the intrinsic magnetic dipole moment of the electron. The two ends of a bar magnet are referred to as poles (not to be confused with monopoles, see Classification below) and may be labeled "north" and "south". In terms of the Earth's magnetic field, they are respectively "north-seeking" and "south-seeking" poles: if the magnet were freely suspended in the Earth's magnetic field, the north-seeking pole would point towards the north and the south-seeking pole would point towards the south. The dipole moment of the bar magnet points from its magnetic south to its magnetic north pole. In a magnetic compass, the north pole of a bar magnet points north. However, that means that Earth's geomagnetic north pole is the south pole (south-seeking pole) of its dipole moment and vice versa.

The only known mechanisms for the creation of magnetic dipoles are by current loops or quantum-mechanical spin since the existence of magnetic monopoles has never been experimentally demonstrated.

Classification

Electric field lines of two opposing charges separated by a finite distance.

Magnetic field lines of a ring current of finite diameter.

Field lines of a point dipole of any type, electric, magnetic, acoustic, etc.

A physical dipole consists of two equal and opposite point charges: in the literal sense, two poles. Its field at large distances (i.e., distances large in comparison to the separation of the poles) depends almost entirely on the dipole moment as defined above. A point (electric) dipole is the limit obtained by letting the separation tend to 0 while keeping the dipole moment fixed. The field of a point dipole has a particularly simple form, and the order-1 term in the multipole expansion is precisely the point dipole field.

Although there are no known magnetic monopoles in nature, there are magnetic dipoles in the form of the quantum-mechanical spin associated with particles such as electrons (although the accurate description of such effects falls outside of classical electromagnetism). A theoretical magnetic point dipole has a magnetic field of exactly the same form as the electric field of an electric point dipole. A very small current-carrying loop is approximately a magnetic point dipole; the magnetic dipole moment of such a loop is the product of the current flowing in the loop and the (vector) area of the loop.

Any configuration of charges or currents has a 'dipole moment', which describes the dipole whose field is the best approximation, at large distances, to that of the given configuration. This is simply one term in the multipole expansion when the total charge ("monopole moment") is 0—as it always is for the magnetic case, since there are no magnetic monopoles. The dipole term is the dominant one at large distances: Its field falls off in proportion to 1/r³, as compared to 1/r⁴ for the next (quadrupole) term and higher powers of 1/r for higher terms, or 1/r² for the monopole term.

Molecular dipoles

See also: Chemical polarity and Dipole moments of molecules

Many molecules have such dipole moments due to non-uniform distributions of positive and negative charges on the various atoms. Such is the case with polar compounds like hydrogen fluoride (HF), where electron density is shared unequally between atoms. Therefore, a molecule's dipole is an electric dipole with an inherent electric field that should not be confused with a magnetic dipole, which generates a magnetic field.

The physical chemist Peter J. W. Debye was the first scientist to study molecular dipoles extensively, and, as a consequence, dipole moments are measured in the non-SI unit named debye in his honor.

For molecules there are three types of dipoles:

Permanent dipoles

These occur when two atoms in a molecule have substantially different electronegativity: One atom attracts electrons more than another, becoming more negative, while the other atom becomes more positive. A molecule with a permanent dipole moment is called a polar molecule. See dipole–dipole attractions.

Instantaneous dipoles

These occur due to chance when electrons happen to be more concentrated in one place than another in a molecule, creating a temporary dipole. These dipoles are smaller in magnitude than permanent dipoles, but still play a large role in chemistry and biochemistry due to their prevalence. See instantaneous dipole.

Induced dipoles

These can occur when one molecule with a permanent dipole repels another molecule's electrons, inducing a dipole moment in that molecule. A molecule is polarized when it carries an induced dipole. See induced-dipole attraction.

More generally, an induced dipole of any polarizable charge distribution ρ (remember that a molecule has a charge distribution) is caused by an electric field external to ρ. This field may, for instance, originate from an ion or polar molecule in the vicinity of ρ or may be macroscopic (e.g., a molecule between the plates of a charged capacitor). The size of the induced dipole moment is equal to the product of the strength of the external field and the dipole polarizability of ρ.

Dipole moment values can be obtained from measurement of the dielectric constant. Some typical gas phase values in debye units are:

• carbon dioxide: 0
• carbon monoxide: 0.112 D
• ozone: 0.53 D
• phosgene: 1.17 D
• NH₃ has a dipole moment of 1.42 D
• water vapor: 1.85 D
• hydrogen cyanide: 2.98 D
• cyanamide: 4.27 D
• potassium bromide: 10.41 D

The linear molecule CO₂ has a zero dipole as the two bond dipoles cancel.

Potassium bromide (KBr) has one of the highest dipole moments because it is an ionic compound that exists as a molecule in the gas phase.

The bent molecule H₂O has a net dipole. The two bond dipoles do not cancel.

The overall dipole moment of a molecule may be approximated as a vector sum of bond dipole moments. As a vector sum it depends on the relative orientation of the bonds, so that from the dipole moment information can be deduced about the molecular geometry.

For example, the zero dipole of CO₂ implies that the two C=O bond dipole moments cancel so that the molecule must be linear. For H₂O the O−H bond moments do not cancel because the molecule is bent. For ozone (O₃) which is also a bent molecule, the bond dipole moments are not zero even though the O−O bonds are between similar atoms. This agrees with the Lewis structures for the resonance forms of ozone which show a positive charge on the central oxygen atom.

Cis isomer, dipole moment 1.90 D

 

Trans isomer, dipole moment zero

An example in organic chemistry of the role of geometry in determining dipole moment is the cis and trans isomers of 1,2-dichloroethene. In the cis isomer the two polar C−Cl bonds are on the same side of the C=C double bond and the molecular dipole moment is 1.90 D. In the trans isomer, the dipole moment is zero because the two C−Cl bonds are on opposite sides of the C=C and cancel (and the two bond moments for the much less polar C−H bonds also cancel).

Another example of the role of molecular geometry is boron trifluoride, which has three polar bonds with a difference in electronegativity greater than the traditionally cited threshold of 1.7 for ionic bonding. However, due to the equilateral triangular distribution of the fluoride ions centered on and in the same plane as the boron cation, the symmetry of the molecule results in its dipole moment being zero.

Quantum mechanical dipole operator

Consider a collection of N particles with charges q_i and position vectors r_i. For instance, this collection may be a molecule consisting of electrons, all with charge −e, and nuclei with charge eZ_i, where Z_i is the atomic number of the i th nucleus. The dipole observable (physical quantity) has the quantum mechanical dipole operator:

${\displaystyle \mathfrak{p}=\sum _{i=1}^N{q}_i{\mathbf{r}}_i.}$

Notice that this definition is valid only for neutral atoms or molecules, i.e. total charge equal to zero. In the ionized case, we have

${\displaystyle \mathfrak{p}=\sum _{i=1}^N{q}_i({\mathbf{r}}_i-{\mathbf{r}}_c),}$

where ${\displaystyle {\mathbf{r}}_c}$ is the center of mass of the molecule/group of particles.

Atomic dipoles

A non-degenerate (S-state) atom can have only a zero permanent dipole. This fact follows quantum mechanically from the inversion symmetry of atoms. All 3 components of the dipole operator are antisymmetric under inversion with respect to the nucleus,

${\displaystyle \mathfrak{I}\mathfrak{p}{\mathfrak{I}}^{-1}=-\mathfrak{p},}$

where ${\displaystyle \mathfrak{p}}$ is the dipole operator and ${\displaystyle \mathfrak{I}}$ is the inversion operator.

The permanent dipole moment of an atom in a non-degenerate state (see degenerate energy level) is given as the expectation (average) value of the dipole operator,

${\displaystyle ⟨\mathfrak{p}⟩=⟨S|\mathfrak{p}|S⟩,}$

where ${\displaystyle |S⟩}$ is an S-state, non-degenerate, wavefunction, which is symmetric or antisymmetric under inversion: ${\displaystyle \mathfrak{I}|S⟩=\pm |S⟩}$. Since the product of the wavefunction (in the ket) and its complex conjugate (in the bra) is always symmetric under inversion and its inverse,

${\displaystyle ⟨\mathfrak{p}⟩=⟨{\mathfrak{I}}^{-1}S|\mathfrak{p}|{\mathfrak{I}}^{-1}S⟩=⟨S|\mathfrak{I}\mathfrak{p}{\mathfrak{I}}^{-1}|S⟩=-⟨\mathfrak{p}⟩}$

it follows that the expectation value changes sign under inversion. We used here the fact that ${\displaystyle \mathfrak{I}}$, being a symmetry operator, is unitary: ${\displaystyle {\mathfrak{I}}^{-1}={\mathfrak{I}}^{\ast }}$ and by definition the Hermitian adjoint ${\displaystyle {\mathfrak{I}}^{\ast }}$ may be moved from bra to ket and then becomes ${\displaystyle {\mathfrak{I}}^{\ast \ast }=\mathfrak{I}}$. Since the only quantity that is equal to minus itself is the zero, the expectation value vanishes,

${\displaystyle ⟨\mathfrak{p}⟩=0.}$

In the case of open-shell atoms with degenerate energy levels, one could define a dipole moment by the aid of the first-order Stark effect. This gives a non-vanishing dipole (by definition proportional to a non-vanishing first-order Stark shift) only if some of the wavefunctions belonging to the degenerate energies have opposite parity; i.e., have different behavior under inversion. This is a rare occurrence, but happens for the excited H-atom, where 2s and 2p states are "accidentally" degenerate (see article Laplace–Runge–Lenz vector for the origin of this degeneracy) and have opposite parity (2s is even and 2p is odd).

Field of a static magnetic dipole

See also: Magnet § Two models for magnets: magnetic poles and atomic currents

Magnitude

The far-field strength, B, of a dipole magnetic field is given by

${\displaystyle B(m,r,\lambda )=\frac{{\mu }_0}{4\pi }\frac{m}{r^3}\sqrt{1+3{\sin }^2(\lambda )},}$

where

B is the strength of the field, measured in teslas

r is the distance from the center, measured in metres

λ is the magnetic latitude (equal to 90° − θ) where θ is the magnetic colatitude, measured in radians or degrees from the dipole axis

m is the dipole moment, measured in ampere-square metres or joules per tesla

μ₀ is the permeability of free space, measured in henries per metre.

Conversion to cylindrical coordinates is achieved using r² = z² + ρ² and

${\displaystyle \lambda =\arcsin \left(\frac{z}{\sqrt{z^2+{\rho }^2}}\right)}$

where ρ is the perpendicular distance from the z-axis. Then,

${\displaystyle B(\rho ,z)=\frac{{\mu }_{0}m}{4\pi {\left(z^2+{\rho }^2\right)}^{\frac{3}{2}}}\sqrt{1+\frac{3z^2}{z^2+{\rho }^2}}}$

Vector form

The field itself is a vector quantity:

${\displaystyle \mathbf{B}(\mathbf{m},\mathbf{r})=\frac{{\mu }_0}{4\pi }\frac{3(\mathbf{m}\cdot \hat{\mathbf{r}})\hat{\mathbf{r}}-\mathbf{m}}{r^3}}$

where

B is the field

r is the vector from the position of the dipole to the position where the field is being measured

r is the absolute value of r: the distance from the dipole

r̂ = r/r is the unit vector parallel to r;

m is the (vector) dipole moment

μ₀ is the permeability of free space

This is exactly the field of a point dipole, exactly the dipole term in the multipole expansion of an arbitrary field, and approximately the field of any dipole-like configuration at large distances.

Magnetic vector potential

The vector potential A of a magnetic dipole is

${\displaystyle \mathbf{A}(\mathbf{r})=\frac{{\mu }_0}{4\pi }\frac{\mathbf{m}\times \hat{\mathbf{r}}}{r^2}}$

with the same definitions as above.

Field from an electric dipole

The electrostatic potential at position r due to an electric dipole at the origin is given by:

${\displaystyle \mathrm{\Phi }(\mathbf{r})=\frac{1}{4\pi {ϵ}_0}\frac{\mathbf{p}\cdot \hat{\mathbf{r}}}{r^2}}$

where p is the (vector) dipole moment, and є₀ is the permittivity of free space.

This term appears as the second term in the multipole expansion of an arbitrary electrostatic potential Φ(r). If the source of Φ(r) is a dipole, as it is assumed here, this term is the only non-vanishing term in the multipole expansion of Φ(r). The electric field from a dipole can be found from the gradient of this potential:

${\displaystyle \mathbf{E}=-\mathrm{\nabla }\mathrm{\Phi }=\frac{1}{4\pi {ϵ}_0}\frac{3(\mathbf{p}\cdot \hat{\mathbf{r}})\hat{\mathbf{r}}-\mathbf{p}}{r^3}-{\delta }^3(\mathbf{r})\frac{\mathbf{p}}{3{ϵ}_0}.}$

This is of the same form of the expression for the magnetic field of a point magnetic dipole, ignoring the delta function. In a real electric dipole, however, the charges are physically separate and the electric field diverges or converges at the point charges. This is different to the magnetic field of a real magnetic dipole which is continuous everywhere. The delta function represents the strong field pointing in the opposite direction between the point charges, which is often omitted since one is rarely interested in the field at the dipole's position. For further discussions about the internal field of dipoles, see or Magnetic moment#Internal magnetic field of a dipole.

Torque on a dipole

Since the direction of an electric field is defined as the direction of the force on a positive charge, electric field lines point away from a positive charge and toward a negative charge.

When placed in a homogeneous electric or magnetic field, equal but opposite forces arise on each side of the dipole creating a torque τ}:

${\displaystyle \mathit{\tau }=\mathbf{p}\times \mathbf{E}}$

for an electric dipole moment p (in coulomb-meters), or

${\displaystyle \mathit{\tau }=\mathbf{m}\times \mathbf{B}}$

for a magnetic dipole moment m (in ampere-square meters).

The resulting torque will tend to align the dipole with the applied field, which in the case of an electric dipole, yields a potential energy of

${\displaystyle U=-\mathbf{p}\cdot \mathbf{E}}$.

The energy of a magnetic dipole is similarly

${\displaystyle U=-\mathbf{m}\cdot \mathbf{B}}$.

Dipole radiation

Modulus of the Poynting vector for an oscillating electric dipole (exact solution). The two charges are shown as two small black dots.

See also: Dipole antenna

In addition to dipoles in electrostatics, it is also common to consider an electric or magnetic dipole that is oscillating in time. It is an extension, or a more physical next-step, to spherical wave radiation.

In particular, consider a harmonically oscillating electric dipole, with angular frequency ω and a dipole moment p₀ along the ẑ direction of the form

${\displaystyle \mathbf{p}(\mathbf{r},t)=\mathbf{p}(\mathbf{r})e^{-i\omega t}=p_0\hat{\mathbf{z}}{e}^{-i\omega t}.}$

In vacuum, the exact field produced by this oscillating dipole can be derived using the retarded potential formulation as:

${\displaystyle \begin{array}{rl}\mathbf{E}& =\frac{1}{4\pi {\epsilon }_0}\left\{\frac{{\omega }^2}{c^{2}r}\left(\hat{\mathbf{r}}\times \mathbf{p}\right)\times \hat{\mathbf{r}}+\left(\frac{1}{r^3}-\frac{i\omega }{c{r}^2}\right)\left(3\hat{\mathbf{r}}\left[\hat{\mathbf{r}}\cdot \mathbf{p}\right]-\mathbf{p}\right)\right\}{e}^{\frac{i\omega r}{c}}{e}^{-i\omega t}\\ \mathbf{B}& =\frac{{\omega }^2}{4\pi {\epsilon }_0{c}^3}(\hat{\mathbf{r}}\times \mathbf{p})\left(1-\frac{c}{i\omega r}\right)\frac{e^{i\omega r/c}}{r}{e}^{-i\omega t}.\end{array}}$

For rω/c ≫ 1, the far-field takes the simpler form of a radiating "spherical" wave, but with angular dependence embedded in the cross-product:

${\displaystyle \begin{array}{rl}\mathbf{B}& =\frac{{\omega }^2}{4\pi {\epsilon }_0{c}^3}(\hat{\mathbf{r}}\times \mathbf{p})\frac{e^{i\omega (r/c-t)}}{r}=\frac{{\omega }^2{\mu }_0{p}_0}{4\pi c}(\hat{\mathbf{r}}\times \hat{\mathbf{z}})\frac{e^{i\omega (r/c-t)}}{r}=-\frac{{\omega }^2{\mu }_0{p}_0}{4\pi c}\sin (\theta )\frac{e^{i\omega (r/c-t)}}{r}\hat{\varphi }\\ \mathbf{E}& =c\mathbf{B}\times \hat{\mathbf{r}}=-\frac{{\omega }^2{\mu }_0{p}_0}{4\pi }\sin (\theta )\left(\hat{\varphi }\times \hat{\mathbf{r}}\right)\frac{e^{i\omega (r/c-t)}}{r}=-\frac{{\omega }^2{\mu }_0{p}_0}{4\pi }\sin (\theta )\frac{e^{i\omega (r/c-t)}}{r}\hat{\theta }.\end{array}}$

The time-averaged Poynting vector

${\displaystyle ⟨\mathbf{S}⟩=\left(\frac{{\mu }_0{p}_0^2{\omega }^4}{32{\pi }^{2}c}\right)\frac{{\sin }^2(\theta )}{r^2}\hat{\mathbf{r}}}$

is not distributed isotropically, but concentrated around the directions lying perpendicular to the dipole moment, as a result of the non-spherical electric and magnetic waves. In fact, the spherical harmonic function (sin θ) responsible for such toroidal angular distribution is precisely the l = 1 "p" wave.

The total time-average power radiated by the field can then be derived from the Poynting vector as

${\displaystyle P=\frac{{\mu }_0{\omega }^4{p}_0^2}{12\pi c}.}$

Notice that the dependence of the power on the fourth power of the frequency of the radiation is in accordance with the Rayleigh scattering, and the underlying effects why the sky consists of mainly blue colour.

A circular polarized dipole is described as a superposition of two linear dipoles.

Van Allen radiation belt

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Van_Allen_radiation_belt

A cross section of Van Allen radiation belts

Van Allen radiation belt is a zone of energetic charged particles, most of which originate from the solar wind, that are captured by and held around a planet by that planet's magnetosphere. Earth has two such belts, and sometimes others may be temporarily created. The belts are named after James Van Allen, who is often credited with their discovery.

Earth's two main belts extend from an altitude of about 640 to 58,000 km (400 to 36,040 mi) above the surface, in which region radiation levels vary. The belts are in the inner region of Earth's magnetic field. They trap energetic electrons and protons. Other nuclei, such as alpha particles, are less prevalent. Most of the particles that form the belts are thought to come from the solar wind while others arrive as cosmic rays. By trapping the solar wind, the magnetic field deflects those energetic particles and protects the atmosphere from destruction.

The belts endanger satellites, which must have their sensitive components protected with adequate shielding if they spend significant time near that zone. Apollo Astronauts going through the Van Allen Belts received a very low and unharmful dose of radiation.

In 2013, the Van Allen Probes detected a transient, third radiation belt, which persisted for four weeks.

Discovery

Kristian Birkeland, Carl Størmer, Nicholas Christofilos, and Enrico Medi had investigated the possibility of trapped charged particles before the Space Age. The second Soviet satellite Sputnik 2 which had detectors designed by Sergei Vernov, followed by the US satellites Explorer 1 and Explorer 3, confirmed the existence of the belt in early 1958, later named after James Van Allen from the University of Iowa. The trapped radiation was first mapped by Explorer 4, Pioneer 3, and Luna 1.

The term Van Allen belts refers specifically to the radiation belts surrounding Earth; however, similar radiation belts have been discovered around other planets. The Sun does not support long-term radiation belts, as it lacks a stable, global dipole field. The Earth's atmosphere limits the belts' particles to regions above 200–1,000 km, (124–620 miles) while the belts do not extend past 8 Earth radii R_E. The belts are confined to a volume which extends about 65° on either side of the celestial equator.

Research

Jupiter's variable radiation belts

The NASA Van Allen Probes mission aims at understanding (to the point of predictability) how populations of relativistic electrons and ions in space form or change in response to changes in solar activity and the solar wind. NASA Institute for Advanced Concepts–funded studies have proposed magnetic scoops to collect antimatter that naturally occurs in the Van Allen belts of Earth, although only about 10 micrograms of antiprotons are estimated to exist in the entire belt.

The Van Allen Probes mission successfully launched on August 30, 2012. The primary mission was scheduled to last two years with expendables expected to last four. The probes were deactivated in 2019 after running out of fuel and are expected to deorbit during the 2030s. NASA's Goddard Space Flight Center manages the Living With a Star program—of which the Van Allen Probes were a project, along with Solar Dynamics Observatory (SDO). The Applied Physics Laboratory was responsible for the implementation and instrument management for the Van Allen Probes.

Radiation belts exist around other planets and moons in the solar system that have magnetic fields powerful enough to sustain them. To date, most of these radiation belts have been poorly mapped. The Voyager Program (namely Voyager 2) only nominally confirmed the existence of similar belts around Uranus and Neptune.

Geomagnetic storms can cause electron density to increase or decrease relatively quickly (i.e., approximately one day or less). Longer-timescale processes determine the overall configuration of the belts. After electron injection increases electron density, electron density is often observed to decay exponentially. Those decay time constants are called "lifetimes." Measurements from the Van Allen Probe B's Magnetic Electron Ion Spectrometer (MagEIS) show long electron lifetimes (i.e., longer than 100 days) in the inner belt; short electron lifetimes of around one or two days are observed in the "slot" between the belts; and energy-dependent electron lifetimes of roughly five to 20 days are found in the outer belt.

Inner belt

Cutaway drawing of two radiation belts around Earth: the inner belt (red) dominated by protons and the outer one (blue) by electrons. Image Credit: NASA

The inner Van Allen Belt extends typically from an altitude of 0.2 to 2 Earth radii (L values of 1.2 to 3) or 1,000 km (620 mi) to 12,000 km (7,500 mi) above the Earth. In certain cases, when solar activity is stronger or in geographical areas such as the South Atlantic Anomaly, the inner boundary may decline to roughly 200 km above the Earth's surface. The inner belt contains high concentrations of electrons in the range of hundreds of keV and energetic protons with energies exceeding 100 MeV—trapped by the relatively strong magnetic fields in the region (as compared to the outer belt).

It is thought that proton energies exceeding 50 MeV in the lower belts at lower altitudes are the result of the beta decay of neutrons created by cosmic ray collisions with nuclei of the upper atmosphere. The source of lower energy protons is believed to be proton diffusion, due to changes in the magnetic field during geomagnetic storms.

Due to the slight offset of the belts from Earth's geometric center, the inner Van Allen belt makes its closest approach to the surface at the South Atlantic Anomaly.

In March 2014, a pattern resembling "zebra stripes" was observed in the radiation belts by the Radiation Belt Storm Probes Ion Composition Experiment (RBSPICE) onboard Van Allen Probes. The initial theory proposed in 2014 was that—due to the tilt in Earth's magnetic field axis—the planet's rotation generated an oscillating, weak electric field that permeates through the entire inner radiation belt. A 2016 study instead concluded that the zebra stripes were an imprint of ionospheric winds on radiation belts.

Outer belt

Laboratory simulation of the Van Allen belt's influence on the Solar Wind; these aurora-like Birkeland currents were created by the scientist Kristian Birkeland in his terrella, a magnetized anode globe in an evacuated chamber

The outer belt consists mainly of high-energy (0.1–10 MeV) electrons trapped by the Earth's magnetosphere. It is more variable than the inner belt, as it is more easily influenced by solar activity. It is almost toroidal in shape, beginning at an altitude of 3 Earth radii and extending to 10 Earth radii (R_E)—13,000 to 60,000 kilometres (8,100 to 37,300 mi) above the Earth's surface. Its greatest intensity is usually around 4 to 5 R_E. The outer electron radiation belt is mostly produced by inward radial diffusion and local acceleration due to transfer of energy from whistler-mode plasma waves to radiation belt electrons. Radiation belt electrons are also constantly removed by collisions with Earth's atmosphere, losses to the magnetopause, and their outward radial diffusion. The gyroradii of energetic protons would be large enough to bring them into contact with the Earth's atmosphere. Within this belt, the electrons have a high flux and at the outer edge (close to the magnetopause), where geomagnetic field lines open into the geomagnetic "tail", the flux of energetic electrons can drop to the low interplanetary levels within about 100 km (62 mi)—a decrease by a factor of 1,000.

In 2014, it was discovered that the inner edge of the outer belt is characterized by a very sharp transition, below which highly relativistic electrons (> 5MeV) cannot penetrate. The reason for this shield-like behavior is not well understood.

The trapped particle population of the outer belt is varied, containing electrons and various ions. Most of the ions are in the form of energetic protons, but a certain percentage are alpha particles and O⁺ oxygen ions—similar to those in the ionosphere but much more energetic. This mixture of ions suggests that ring current particles probably originate from more than one source.

The outer belt is larger than the inner belt, and its particle population fluctuates widely. Energetic (radiation) particle fluxes can increase and decrease dramatically in response to geomagnetic storms, which are themselves triggered by magnetic field and plasma disturbances produced by the Sun. The increases are due to storm-related injections and acceleration of particles from the tail of the magnetosphere. Another cause of variability of the outer belt particle populations is the wave-particle interactions with various plasma waves in a broad range of frequencies. 

On February 28, 2013, a third radiation belt—consisting of high-energy ultrarelativistic charged particles—was reported to be discovered. In a news conference by NASA's Van Allen Probe team, it was stated that this third belt is a product of coronal mass ejection from the Sun. It has been represented as a separate creation which splits the Outer Belt, like a knife, on its outer side, and exists separately as a storage container of particles for a month's time, before merging once again with the Outer Belt.

The unusual stability of this third, transient belt has been explained as due to a 'trapping' by the Earth's magnetic field of ultrarelativistic particles as they are lost from the second, traditional outer belt. While the outer zone, which forms and disappears over a day, is highly variable due to interactions with the atmosphere, the ultrarelativistic particles of the third belt are thought not to scatter into the atmosphere, as they are too energetic to interact with atmospheric waves at low latitudes. This absence of scattering and the trapping allows them to persist for a long time, finally only being destroyed by an unusual event, such as the shock wave from the Sun.

Flux values

In the belts, at a given point, the flux of particles of a given energy decreases sharply with energy.

At the magnetic equator, electrons of energies exceeding 5000 keV (resp. 5 MeV) have omnidirectional fluxes ranging from 1.2×10⁶ (resp. 3.7×10⁴) up to 9.4×10⁹ (resp. 2×10⁷) particles per square centimeter per second.

The proton belts contain protons with kinetic energies ranging from about 100 keV, which can penetrate 0.6 µm of lead, to over 400 MeV, which can penetrate 143 mm of lead.

Most published flux values for the inner and outer belts may not show the maximum probable flux densities that are possible in the belts. There is a reason for this discrepancy: the flux density and the location of the peak flux is variable, depending primarily on solar activity, and the number of spacecraft with instruments observing the belt in real time has been limited. The Earth has not experienced a solar storm of Carrington event intensity and duration, while spacecraft with the proper instruments have been available to observe the event.

Radiation levels in the belts would be dangerous to humans if they were exposed for an extended period of time. The Apollo missions minimised hazards for astronauts by sending spacecraft at high speeds through the thinner areas of the upper belts, bypassing inner belts completely, except for the Apollo 14 mission where the spacecraft traveled through the heart of the trapped radiation belts.

• Flux values, normal solar conditions
• 
  AP8 MIN omnidirectional proton flux ≥ 100 keV
   
• 
  AP8 MIN omnidirectional proton flux ≥ 1 MeV
• 
  AP8 MIN omnidirectional proton flux ≥ 400 MeV

Antimatter confinement

In 2011, a study confirmed earlier speculation that the Van Allen belt could confine antiparticles. The Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) experiment detected levels of antiprotons orders of magnitude higher than are expected from normal particle decays while passing through the South Atlantic Anomaly. This suggests the Van Allen belts confine a significant flux of antiprotons produced by the interaction of the Earth's upper atmosphere with cosmic rays. The energy of the antiprotons has been measured in the range from 60 to 750 MeV.

Research funded by the NASA Institute for Advanced Concepts concluded that harnessing these antiprotons for spacecraft propulsion would be feasible. Researchers believed that this approach would have advantages over antiproton generation at CERN because collecting the particles in situ eliminates transportation losses and costs. Jupiter and Saturn are also possible sources, but the Earth belt is the most productive. Jupiter is less productive than might be expected due to magnetic shielding from cosmic rays of much of its atmosphere. In 2019, CMS announced that the construction of a device that would be capable of collecting these particles has already begun. NASA will use this device to collect these particles and transport them to institutes all around the world for further examination. These so-called "antimatter containers" could be used for industrial purposes as well in the future.

Implications for space travel

Orbit size comparison of GPS, GLONASS, Galileo, BeiDou-2, and Iridium constellations, the International Space Station, the Hubble Space Telescope, and geostationary orbit (and its graveyard orbit), with the Van Allen radiation belts and the Earth to scale.

The Moon's orbit is around 9 times as large as geostationary orbit. (In the SVG file, hover over an orbit or its label to highlight it; click to load its article.)

Spacecraft travelling beyond low Earth orbit enter the zone of radiation of the Van Allen belts. Beyond the belts, they face additional hazards from cosmic rays and solar particle events. A region between the inner and outer Van Allen belts lies at 2 to 4 Earth radii and is sometimes referred to as the "safe zone".

Solar cells, integrated circuits, and sensors can be damaged by radiation. Geomagnetic storms occasionally damage electronic components on spacecraft. Miniaturization and digitization of electronics and logic circuits have made satellites more vulnerable to radiation, as the total electric charge in these circuits is now small enough so as to be comparable with the charge of incoming ions. Electronics on satellites must be hardened against radiation to operate reliably. The Hubble Space Telescope, among other satellites, often has its sensors turned off when passing through regions of intense radiation. A satellite shielded by 3 mm of aluminium in an elliptic orbit (200 by 20,000 miles (320 by 32,190 km)) passing the radiation belts will receive about 2,500 rem (25 Sv) per year. (For comparison, a full-body dose of 5 Sv is deadly.) Almost all radiation will be received while passing the inner belt.

The Apollo missions marked the first event where humans traveled through the Van Allen belts, which was one of several radiation hazards known by mission planners. The astronauts had low exposure in the Van Allen belts due to the short period of time spent flying through them.

Astronauts' overall exposure was actually dominated by solar particles once outside Earth's magnetic field. The total radiation received by the astronauts varied from mission-to-mission but was measured to be between 0.16 and 1.14 rads (1.6 and 11.4 mGy), much less than the standard of 5 rem (50 mSv) per year set by the United States Atomic Energy Commission for people who work with radioactivity.

Causes

It is generally understood that the inner and outer Van Allen belts result from different processes. The inner belt is mainly composed of energetic protons produced from the decay of so-called "albedo" neutrons, which are themselves the result of cosmic ray collisions in the upper atmosphere. The outer Van Allen belt consists mainly of electrons. They are injected from the geomagnetic tail following geomagnetic storms, and are subsequently energized through wave-particle interactions.

In the inner belt, particles that originate from the Sun are trapped in the Earth's magnetic field. Particles spiral along the magnetic lines of flux as they move "latitudinally" along those lines. As particles move toward the poles, the magnetic field line density increases, and their "latitudinal" velocity is slowed and can be reversed, deflecting the particles back towards the equatorial region, causing them to bounce back and forth between the Earth's poles. In addition to both spiralling around and moving along the flux lines, the electrons drift slowly in an eastward direction, while the protons drift westward.

The gap between the inner and outer Van Allen belts is sometimes called the "safe zone" or "safe slot", and is the location of medium Earth orbits. The gap is caused by the VLF radio waves, which scatter particles in pitch angle, which adds new ions to the atmosphere. Solar outbursts can also dump particles into the gap, but those drain out in a matter of days. The VLF radio waves were previously thought to be generated by turbulence in the radiation belts, but recent work by J.L. Green of the Goddard Space Flight Center compared maps of lightning activity collected by the Microlab 1 spacecraft with data on radio waves in the radiation-belt gap from the IMAGE spacecraft; the results suggest that the radio waves are actually generated by lightning within Earth's atmosphere. The generated radio waves strike the ionosphere at the correct angle to pass through only at high latitudes, where the lower ends of the gap approach the upper atmosphere. These results are still being debated in the scientific community.

Proposed removal

Draining the charged particles from the Van Allen belts would open up new orbits for satellites and make travel safer for astronauts.

High Voltage Orbiting Long Tether, or HiVOLT, is a concept proposed by Russian physicist V. V. Danilov and further refined by Robert P. Hoyt and Robert L. Forward for draining and removing the radiation fields of the Van Allen radiation belts that surround the Earth.

Another proposal for draining the Van Allen belts involves beaming very-low-frequency (VLF) radio waves from the ground into the Van Allen belts.

Draining radiation belts around other planets has also been proposed, for example, before exploring Europa, which orbits within Jupiter's radiation belt.

As of 2014, it remains uncertain if there are any negative unintended consequences to removing these radiation belts.