## Characteristics of typical radiation belt charged particles

The following table appears in  . The gyration numbers seem to be incorrect for the 500km altitude. Depending on the magnetic latitude and pitch angle of these "typical particles", the table values for the gyration period are between 2.3 and 5.0 too large, as if the B field is 3x too small or the altitude is 2800 km instead of 500km . This does not even occur over the south Atlantic anomaly, which brings the lower field down only 500km or so.

 Particle 1 MeV 10 MeV electron proton Range in aluminium (mm) 2 0.4 Peak equatorial omni-directional flux (cm-2 s-1) 4E6 3.4E5 Radial location (L) of peak flux (Earth-radii) 4.4 1.7 Radius of gyration (km) 500 km 0.6 50 20000 km 10 880 Gyration period (s) 500 km 1E-5 7E-3 20000 km 2E-4 0.13 Bounce period (s) 500 km 0.1 0.65 20000 km 0.3 1.7 Longitudinal drift period (min) 500 km 10 3 20000 km 3.5 1.1

Constants:

 Magnetic field constant Tesla 3.0037e-05 B0 Unit charge Colombs 1.6021e-19 q Joules per MeV J/MeV 1.6021e-13 Earth radius m 6.37821e+06 RE Speed of Light m/s 2.9979e+08 c

Let's compute some numbers at 500km altitude:

 ratio 1.078 ratio = 1 + alt/RE L @ 0 degrees magnetic latitude 1.078 L=ratio L @ 90 degrees magnetic latitude infinite B @ 0 degrees magnetic latitude Tesla 2.40E-05 Blat0=B0/ratio3 . . . * sqrt( 4-3 ratio/L ) B @ 90 degrees magnetic latitude Tesla 4.79E-05 Blat90=2B0/ratio3 . . . * sqrt( 4-3 ratio/inf ) Particle electron proton Kinetic Energy MeV 1 10 Kinetic Energy J 1.6021E-13 1.6021E-12 Ek Rest Mass kg 9.1094E-31 1.6726E-27 m0 Mass Energy J 8.1871E-14 1.5033E-10 E0=m0c2 Relativistic Momentum kg m/s 7.60E-22 7.34E-20 p=sqrt( 2E0Ek+Ek2)/c Lorentz Factor 2.957 1.0107 gamma=1/sqrt(1-(v/c)2) Velocity m/s 2.82E+08 4.34E+07 v=pc2/(Ek+E0) "Relativistic Mass" kg 2.69E-30 1.69E-27 mr=m0 gamma Gyration Period/Field T-s 1.06E-10 6.63E-08 2pi mr / q Gyration Period @ 0 degrees s 4.41E-06 2.77E-03 Period = 2pi mr / q Blat0 Gyration Period @ 90 degrees s 2.21E-06 1.39E-03 Period = 2pi mr / q Blat90 Gyration Period from table s _1E-5_ _7E-3_ 10000nT, 2800km altitude Blat0???

Calculations based on the equations in Pisacane  and the equations for relativistic momentum and energy scattered around Wikipedia.

Without the pitch angle and the L value (or the magnetic latitude), I can't guess at the bounce period (there are values that yield the above results). Plausible values of pitch angle yield gyration radii that are larger than those for 500km in the table.

The 20000km numbers ( the altitude of most nav-sats ) are plausible.

What am I missing here?

### References:

TypicalParticles (last edited 2010-08-13 06:03:33 by KeithLofstrom)