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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.
Line 12: Line 15:
|| @ 500 km || 0.6 || 50 ||
|| @ 20000 km || 10 || 880 ||		 ||   500 km || 0.6 || 50 ||
||   20000 km || 10 || 880 ||
Line 15: Line 18:
|| @ 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 18: Line 21:
|| @ 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 21: Line 24:
|| @ 500 km   || 10 || 3 ||
|| @ 20000 km   || 3.5 || 1.1 ||		 ||     500 km || 10 || 3 ||
||     20000 km || 3.5 || 1.1 ||
Line 26: Line 29:
|| 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 ||		 || Magnetic field constant || Tesla || 3.0037E-05 || B,,0,, ||
|| Unit charge || Colombs || 1.6021E-19 || q ||
|| Joules per MeV || J/MeV || 1.6021E-13 ||
|| Earth radius || m || 6378210.00 || R,,E,, ||
|| Speed of Light || m/s || 2.9979E+08 || c ||
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|| 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 ||
 || ratio || |||| 1.078          || ratio = 1 + alt/R,,E,, ||
|| L @  0 degrees magnetic latitude || |||| 1.078 || L=ratio ||
|| L @ 90 degrees magnetic latitude || |||| infinite          ||
|| B @ 0 degrees magnetic latitude || Tesla |||| 2.40E-05          || B,,lat0,,=B,,0,,/ratio^^3 ||
|| B @ 90 degrees magnetic latitude || Tesla |||| 4.79E-05          || B,,lat90,,=2B,,0,,/ratio^^3 ||
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|| 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 ||		 || Kinetic Energy || J || 1.6021E-13 || 1.6021E-12 || E,,k,, ||
|| Rest Mass || kg || 9.1094E-31 || 1.6726E-27 || m,,0,, ||
|| Mass Energy || J || 8.1871E-14 || 1.5033E-10 || E,,0,,=m,,0,,c^2^ ||
|| Relativistic Momentum || kg m/s || 7.60E-22 || 7.34E-20  || p=sqrt( 2E,,0,,E,,k,,+E,,k,,^2^)/c ||
|| Lorentz Factor || || 2.957 || 1.0107 || gamma=1/sqrt(1-(v/c)^2^) ||
|| Velocity || m/s || 2.82E+08 || 4.34E+07 || v=pc^2^/(E,,k,,+E,,0,,) ||
|| "Relativistic Mass" || kg || 2.69E-30 || 1.69E-27   || m,,r,,=m,,0,, gamma ||
|| Gyration Period/Field || T-s || 1.06E-10 || 6.63E-08 || 2pi m,,r,, / q ||
|| Gyration Period @ 0 degrees || s || 4.41E-06 || 2.77E-03 || Period = 2pi m,,r,, / q B,,lat0 ||
|| Gyration Period @ 90 degrees || s || 2.21E-06 || 1.39E-03 || Period = 2pi m,,r,, / q B,,lat90 ||
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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 scattered around Wikipedia.
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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.

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:

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

6378210.00

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

B @ 90 degrees magnetic latitude

Tesla

4.79E-05

Blat90=2B0/ratio3

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 B,,lat0

|| Gyration Period @ 90 degrees || s || 2.21E-06 || 1.39E-03 || Period = 2pi mr / q B,,lat90 ||

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

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