Transcript A Schematic View of the Locations of Radiation Belts

Aerospace Environment
ASEN-5335
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Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee)
Contact info: e-mail: [email protected] (preferred)
phone: 2-3514, or 5-0523, fax: 2-6444,
website: http://lasp.colorado.edu/~lix
Instructor’s hours: 9:00-11:00 pm Wed at ECOT 534;
Tue & Thu, after class.
TA’s office hours: 3:15-5:15 pm Wed at ECAE 166
Read Chapter 1 & 2.
1st quiz next Tuesday
The Motion of Charged Particles in Magnetic Fields
In a constant magnetic field without external forces, there exists a balance between the Lorenz
force and the centrifugal force which results in circular motion:
Gyrofrequency:
=qB/m
Gyroradius:
r=v/=mv/qB
Pitch angle:
= tan-1 (v /v)
Now we will consider the influences of an external force and a non-uniform B-field. Five cases:
 External force independent of charge
 External force dependent on charge
 Non-uniform B-field
 Curvature in B-field geometry
 Converging/diverging field lines.
1. Charge-independent force  Charge-dependent drift
Such an example is the gravitational force.
r=v/=mv/qB
This represents current flows to the right
2. Charge-dependent force  Charge-independent drift
If we replace by F=qE, in this case, vd = FxB/qB2 = ExB/B2 which is charge independent
drift. Therefore both + and – particles move in the same direction and there is no current.
r=v/=mv/qB
3. Non-uniform magnetic field
Force in a non-uniform magnetic field
Pitch angle: = tan-1 (v /v)
Particle’s energy: eV, keV, MeV, GeV. 1 eV=1.6022x10-19 Joule
Magnetic moment - definition
4. Magnetic field curvature
As a gyrorating particle moves
along a B-field that is curved,
some additional force must act
on the particle and make it turn
and follow the field line geometry.
vd = FxB/qB2
Since this depends on the
sign of q, positive and
negative particles drift in
opposite directions due to
the curvature  current.
5. Converging/diverging field lines
 For a proton in a diverging B-field as shown in the figure, the force acting at right angles to the Bvector does not lie in the plane of circular motion of the charged particle. Rather, the net force is
now in the direction of weaker B-field (diverging field lines). The same holds true for an electron.
 When the magnitude and duration of the force are sufficient to actually cause the charged particle
to reverse direction of motion along the line of magnetic force, the effect is known as mirroring, and
the location of the particle’s path reversal is known as the mirror point for that particle.
F=-B
Charged Particle Motions in Earth’s Magnetic Field
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Gyromotion motion: =p2/2mB (1st), T_g~10-3 sec
Bounce Motion: J= p||ds
(2nd), T_b~100 sec
Drift motion: =BdA
(3rd) , T_d~103 sec
Dipole magnetic field: Br=-2B0cos (RE/r)3
B=-B0sin (RE/r)3
A Schematic View of the Locations of Radiation Belts
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Blue: inner belt, >100MeV
protons, rather stable
Purple: outer belt, 100s keV
and MeV electrons and ions,
not stable at all
Slot region in between
Yellow: ACRs, stable
White line: Earth’s magnetic
field, approx. by a dipole field