Aerospace EnvironmentASEN-5335

Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee) Contact info: e-mail: lix@lasp.colorado.edu (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.

This represents current flows to the right

r=v/=mv/qB

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.

Since this depends on the sign of q, positive and negative particles drift in opposite directions due to the curvature current.

vd = FxB/qB2

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 B-vector 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

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

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