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Alex
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Radiation belt particle energization occurs even ifAny process that is slow compared to the bounce- and gyro- timescales but comparable to the drift timescale can conserve the first two invariants are conserved, provided thatbut breaks the third invariant (given by the total magnetic flux enclosed by the trapped particle due to its gradient-curvature drift motion across field lines around the magnetized body) is violated. In this case, both betatron and Fermi acceleration can occur: betatron acceleration occurs because of the increase in magnetic field affecting the perpendicular energy to maintain a constant first invariant; while Fermi acceleration occurs due to the change in location of the mirror points (along the guiding center bounce path ~ a field line, due to the mirror force), which is required to maintain a constant second invariant. The second invariant is conserved as long as this motion (i.e. the change in location of the mirror point) occurs on a timescale that is much larger than a bounce period. Any process that is slow compared to the bounce- and gyro- timescales but fast compared to the drift timescale can conserve the first two invariants but breaks the third. Such processes (in Earth's magnetosphere) include the arrival of an interplanetary shock, storm-time compression of the magnetosphere, and also sub-storm dipolarization events on the night-side. MHD waves generated by these processes can also interact with particles on the drift timescale, causing drift-resonances and radial transport (or diffusion in the case of multiple waves).

Radiation belt particle energization occurs even if the first two invariants are conserved, provided that the third invariant (given by the total magnetic flux enclosed by the trapped particle due to its gradient-curvature drift motion across field lines around the magnetized body) is violated. In this case, both betatron and Fermi acceleration can occur: betatron acceleration occurs because of the increase in magnetic field affecting the perpendicular energy to maintain a constant first invariant; while Fermi acceleration occurs due to the change in location of the mirror points (along the guiding center bounce path ~ a field line, due to the mirror force), which is required to maintain a constant second invariant. The second invariant is conserved as long as this motion (i.e. the change in location of the mirror point) occurs on a timescale that is much larger than a bounce period. Any process that is slow compared to the bounce- and gyro- timescales but fast compared to the drift timescale can conserve the first two invariants but breaks the third. Such processes (in Earth's magnetosphere) include the arrival of an interplanetary shock, storm-time compression of the magnetosphere, and also sub-storm dipolarization events on the night-side. MHD waves generated by these processes can also interact with particles, causing drift-resonances and radial transport (or diffusion in the case of multiple waves).

Any process that is slow compared to the bounce- and gyro- timescales but comparable to the drift timescale can conserve the first two invariants but breaks the third invariant (given by the total magnetic flux enclosed by the trapped particle due to its gradient-curvature drift motion across field lines around the magnetized body). Such processes (in Earth's magnetosphere) include the arrival of an interplanetary shock, storm-time compression of the magnetosphere, and also sub-storm dipolarization events on the night-side. MHD waves generated by these processes can also interact with particles on the drift timescale, causing drift-resonances and radial transport (or diffusion in the case of multiple waves).

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Alex
Alex
  • 1
  • 1

Radiation belt particle energization occurs even if the first two invariants are conserved, provided that the third invariant (given by the total magnetic flux enclosed by the trapped particle due to its gradient-curvature drift motion across field lines around the magnetized body) is violated. In this case, both betatron and Fermi acceleration can occur: betatron acceleration occurs because of the increase in magnetic field affecting the perpendicular energy to maintain a constant first invariant; while Fermi acceleration occurs due to the change in location of the mirror points (along the guiding center bounce path ~ a field line, due to the mirror force), which is required to maintain a constant second invariant. The second invariant is conserved as long as this motion (i.e. the change in location of the mirror point) occurs on a timescale that is much larger than a bounce period. Any process that is slow compared to the bounce- and gyro- timescales but fast compared to the drift timescale can conserve the first two invariants but breaks the third. Such processes (in Earth's magnetosphere) include the arrival of an interplanetary shock, storm-time compression of the magnetosphere, and also sub-storm dipolarization events on the night-side. MHD waves generated by these processes can also interact with particles, causing drift-resonances and radial transport (or diffusion in the case of multiple waves).