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| [1] [[ http:// | ECSS-E-10-04A, 21 January 2000, Table 28, page 94 ]] | [1] [[ http://www.everyspec.com%2FESA%2Fdownload.php%3Fspec%3DECSS-E-10-04A.014020.pdf&ei=8ixjTPPJKoSdlgfE_c2DAwusg=AFQjCNFOaH2USoAVv9yBHI7Zy826QMggpw&sig2=nrEMcMDTvsEIVOrC0ykorQ | ECSS-E-10-04A, 21 January 2000, Table 28, page 94 ]] |
Characteristics of typical radiation belt charged particles
The following table appears in [1][2][3] . The gyration numbers seem to be incorrect for the 500km altitude.
|
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:
B_0_ Magnetic field constant |
Tesla |
3.0037E-05 |
Unit charge |
Colombs |
1.6021E-19 |
Joules per MeV |
J/MeV |
1.6021E-13 |
Re Earth radius |
m |
6378210.00 |
C Speed of Light |
m/s |
2.9979E+08 |
Let's compute some numbers at 500km altitude:
L @ 0 degrees magnetic |
|
1.078 |
L @ 90 degrees magnetic |
|
infinite |
B @ 0 degrees magnetic |
Tesla |
2.40E-05 |
B @ 90 degrees magnetic |
Tesla |
4.79E-05 |
|
Particle |
||
electron |
proton |
||
Kinetic Energy |
MeV |
1 |
10 |
Kinetic Energy |
J |
1.6021E-13 |
1.6021E-12 |
Mass |
kg |
9.1094E-31 |
1.6726E-27 |
Mass Energy |
J |
8.1871E-14 |
1.5033E-10 |
Relativistic Momentum |
kg m/s |
7.60E-22 |
7.34E-20 |
Lorentz Factor |
|
2.957 |
1.0107 |
Velocity |
m/s |
2.82E+08 |
4.34E+07 |
"Relativistic Mass" |
kg |
2.69E-30 |
1.69E-27 |
Gyr Period/Field |
T-s |
1.06E-10 |
6.63E-08 |
Gyr Period @ 0 degrees |
s |
4.41E-06 |
2.77E-03 |
Gyr Period @ 90 degrees |
s |
2.21E-06 |
1.39E-03 |
Gyr Period from table |
s |
1E-5 |
7E-3 |
So, depending on the magnetic latitude of this "typical particle", the table values for the gyration period are between 2.3 and 5.0 too large.
Calculations based on the equations in Pisacane [3] and the equations for relativistic momentum and energy on Wikipedia
What am I missing here?
References:
[1] ECSS-E-10-04A, 21 January 2000, Table 28, page 94 [2] ECSS-E-ST-10-04C, 15 November 2008, Table I-1, page 162 [3] "The Space Environment and Its Effects on Space Systems", Vincent L. Piscane, AIAA 2008, Table 6.5, page 135