Diff for "TypicalParticles"

Differences between revisions 11 and 12

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. 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.

	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:

B₀ 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 latitude		1.078
L @ 90 degrees magnetic latitude		infinite
B @ 0 degrees magnetic latitude	Tesla	2.40E-05
B @ 90 degrees magnetic latitude	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
Gyration Period/Field	T-s	1.06E-10	6.63E-08
Gyration Period @ 0 degrees	s	4.41E-06	2.77E-03
Gyration Period @ 90 degrees	s	2.21E-06	1.39E-03
Gyration Period from table	s	1E-5	7E-3

Calculations based on the equations in Pisacane [3] 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:

[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. Pisacane, AIAA 2008, Table 6.5, page 135

-  ⇤ ← Revision 11 as of 2010-08-11 23:23:17 → 
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  Editor: KeithLofstrom
  Comment:
+   ← Revision 12 as of 2010-08-12 01:26:41 → ⇥
  Size: 4487
  Editor: KeithLofstrom
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 14:
-||   @ 500 km                                           || 0.6      || 50      ||
||   @ 20000 km                                         || 10       || 880     ||
+||     500 km                                           || 0.6      || 50      ||
||     20000 km                                         || 10       || 880     ||
 Line 17:
-||   @ 500 km                                           || 1E-5     || 7E-3    ||
||   @ 20000 km                                         || 2E-4     || 0.13    ||
+||     500 km                                           || 1E-5     || 7E-3    ||
||     20000 km                                         || 2E-4     || 0.13    ||
 Line 20:
-|| @ 500 km                                             || 0.1      || 0.65    ||
|| @ 20000 km                                           || 0.3      || 1.7     ||
+||     500 km                                           || 0.1      || 0.65    ||
||     20000 km                                         || 0.3      || 1.7     ||
 Line 23:
-|| @ 500 km                                             || 10       || 3       ||
|| @ 20000 km                                           || 3.5      || 1.1     ||
+||     500 km                                           || 10       || 3       ||
||     20000 km                                         || 3.5      || 1.1     ||
 Line 28:
-|| 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 ||
+|| 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 ||
 Line 36:
-|| L @  0 degrees magnetic latitude ||       || 1.078      ||
|| L @ 90 degrees magnetic latitude ||       || infinite   ||
|| B @  0 degrees magnetic latitude || Tesla || 2.40E-05   ||
|| B @ 90 degrees magnetic latitude || Tesla || 4.79E-05   ||
+|| L @  0 degrees magnetic latitude ||       |||| 1.078      ||
|| L @ 90 degrees magnetic latitude ||       |||| infinite   ||
|| B @  0 degrees magnetic latitude || Tesla |||| 2.40E-05   ||
|| B @ 90 degrees magnetic latitude || Tesla |||| 4.79E-05   ||