Differences between revisions 4 and 5
Revision 4 as of 2010-08-11 22:27:12
Size: 2723
Comment:
Revision 5 as of 2010-08-11 22:58:17
Size: 3848
Comment:
Deletions are marked like this. Additions are marked like this.
Line 32: Line 32:
Let's compute some more numbers at 500km altitude: Let's compute some numbers at 500km altitude:
Line 34: Line 34:
||||<|2> |||| Particle ||
|| electron || proton ||
|| Kinetic Energy || MeV || 1 || 10 ||
|| Kinetic Energy || J || 1.6021E-13 || ||
|| Mass || kg || 9.1094E-31 || 1.6726E-27 ||
|| Mass Energy || J || 8.1871E-14 || 1.5033E-10 ||
|| Relativistic Momentum || kg m/s || 7.5991E-22 || 7.3403E-20 ||
|| Lorentz Factor || || 2.9569 || 1.0107 ||
|| Velocity || m/s || 2.8213E+08 || 4.3422E+07 ||
|| "Relativistic Mass" || kg || 2.6935E-30 || 1.6904E-27 ||
|| 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 ||

||||<|2> |||| 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] [[ http:// | ECSS-E-10-04A, 21 January 2000, Table 28, page 94 ]]
[2] [[ http:// | 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

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

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