C. Störmer, 1904; 1929; 1950

Allowed and forbidden regions for charged particles coming from infinity (e.g. SEP & CR)

in vicinity of magnetic dipole

Lemaître and Vallarta, 1932

Lemaire,J. , Effects of a southward magnetic field on Störmer’s allowed regions, Adv. Space Research, 31, N° 5, 1131, 2003

Lemaire et al., Journal Atmospheric Solar Terrestrial Physics, 67, 719, 2005

Magnetic field : IGRFBz = 0

Oxygen ion• 10 MeV • ppa 20°• L= 2

Periodicities• Gyro : 0.056 s• Bounce : 4.8 s• Drift : 154 s

Magnetic field: dipoleBz = 0 & EF = 0

Oxygen ion• 10 MeV • ppa 20°• L= 2 Periodicities• Gyro : 0.054 s• Bounce : 4.9 s• Drift : 154 s

• Bounce phase beating: 102 s (after 23 bounces)

Magnetic field: Dipole+ variable Bz: (alike geomagnetic storm): • Dst: -100 nT• No waves

Oxygen ion • 10 MeV; • ppa 20°• L = 2 Periodicities: • Gyro: 0.054 s• Bounce: 4.9 s• Drift : 157 s

• Bounce phase beatingafter 23 bounces

Magnetic field: Dipole+ variable Bz: (alike geomagnetic storm): • Dst: -100 nT• No waves

Oxygen ion • 1 MeV; • ppa 20°• L = 2 Periodicities: • Gyro: 0.12s• Bounce: 13 s• Drift : 1570 s

Drift velocity is 10 times smaller thus the number of mp is reduced by the same factor

Smaller dispersion of Bm ; GyroRadius smaller by factor 3.3 Equatorial gyroperiod of 0+ is 16 times smaller than that of protons; therefore they are more prompt to violate the second Alfvén condition for adiabatic motion / first order guiding center approximation.

Note however again the strict adiabatic recovery of kinetic energy

SUMMARY OF SIMULATION RESULTS

•Betatron acceleration/deceleration remains the major mechanism for particle mirroring close to equatorial plane

• Fermi-like deceleration/acceleration is also an essential mechanism during magnetic storms

• ULF waves (Pi2) are certainly also good candidates to accelerate particles to higher energies

• For all these mechanisms kinetic energy and adiabatic invariants change in a reversible way, provided Alfvén conditions are verified

• The energy of trapped particles is not conserved when elmg waves are in resonance with their gyro period at any place during its bounce motion, or during its drift motion.

• it has not yet been convincingly demonstrated that these resonant wp-interactions alonoe can accelerate all the particles simultaneously up to MeV energies,in a time as short as observed (recovery phase).

PROSPECTIVE

During main phases of magnetic storms, mirror point of all charged particles of any energy and pitch angle are lifted up to higher altitudes (1);

their rates of collisions with ionospheric and atmospheric constituents are then reduced (2);

their kinetic energy is then also reduced (3); their rate of precipitation into the atmosphere are reduced (4);

they accumulate closer to equatorial region (5); this storage is enhanced by non-resonant pitch-angle scattering, and w-p interactions with all kinds of elmg waves of a wide range of frequencies and phases (6).

PROSPECTIVE ( DURING RECOVERY PHASES)

During recovery phases the altitudes of mirror points decrease for particles of all energies and all pseudo pitch angles; particles are re-energetized (7);

flux of trapped particles at lower altitudes is then enhanced (8);

precipitation into atmospheric is enhanced due to the widening of the loss cone angle, and non-resonant pitch angle scattering with VLF waves, EMIC waves and others …(8)

Simple explanations are simpler to understand