At the midplane of a magnetic mirror with mirror ratio

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · The plasma state and single-particle motion · The plasma state and single-particle motion

Plasma Physics, Ch Slow changes and what survives them: adiabatic invariants, mirrors and trapped orbits

Problem

R_{\rm mir}

, a population is not isotropic: the number of particles per unit solid angle is proportional to

\sin^2\alpha_0

, so directions nearly across the field are favoured. ((a)) Derive the fraction of this population that lies inside the loss cone, in terms of

c=\cos\alpha_{\rm lc}=(1-1/R_{\rm mir})^{1/2}

. ((b)) Check your result at

R_{\rm mir}=1

and as

R_{\rm mir}\to\infty

. ((c)) Evaluate it for

R_{\rm mir}=4

, and compare it with the isotropic lost fraction at the same mirror ratio. ((d)) What mirror ratio would an isotropic population need for its lost fraction to be as small as your answer to (c)?

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