Aerospace Environment ASEN-5335 Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee) Contact info: phone: , or , fax: , website: 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. 1 st 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, v d = FxB/qB 2 = ExB/B 2 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=1.6022x 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. v d = FxB/qB 2

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:  =p 2  /2mB (1st), T_g~10 -3 sec Bounce Motion: J=  p || ds (2nd), T_b~10 0 sec Drift motion:  =  BdA (3rd), T_d~10 3 sec Dipole magnetic field: B r =-2B 0 cos  (R E /r) 3 B  =-B 0 sin  (R E /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