Plasma in time-varying B-field

Particle acceleration Consider a plasma in a homogeneous magnetic field changing in time We then have: Using Stokes theorem: The induced E-field will accelerate or decelerate the particles:

Conservation of μ μ is conserved in a slowly varying B-field: The magnetic flux enclosed in a gyro-orbit is also enclosed:

Adiabatic compression Consider a cylindrical plasma in a changing magnetic field: And for the radial drift velocity: Time derivative of the amount of magnetic flux enclosed by plasma:

Force in parallel direction Force from B-field gradient: Plus electric field: Energy conservation: Eq. for v-parrallel:

Guiding center motion in slowly varying fields

Time-varying E-field

Dielectric constant