The Motion of a Charged Particle in a Nearly Axisymmetric Magnetic Field

H Weitzner

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Since we wish to follow the flux surface on which a particle lies we must determine the cortbination e^ p-^ + eq2 with sont care. We see that eV2 p^ + e q2 = G^/2 p^ + e q2 + 0{e^) (A3) and that the error term is just a point function of the coordinates, independent of tine and not equivalent to a particle drift across a flux surface. After the transformations H = (1/2) I (E q§ + 2F q3f53 + G p§) + R|/e (q2 + A^)}^\ + /e p^^e (q2+A^ ) + e T^/l + 0(e^/2^ ^ (A4) where T^ = IR p§ - 2We (q2+A^ )] (...A;^, e^3+\, eP3+\^, 9 ^ +(/e (q2+A^ )]\^^^h^^, X^2^^, ^\-^, x\^ + ^^, ^\ - f^, x\+ E^, „P3+ E^;, q3)q§ -51- + 2(F, ,i. A, x - ^X^ + ^4'P3 -^ F^^q3)q3P3 + (^, A - ^, X\ ■" "^'. 'PPS + G^;^q3)p-§ (A5) +2 E q3(\, ^A^- \, x% + ^, ^^3+ \, X^3) + P3(\, A " %, X\ + %, >|;^3 -^ %, X^3)^ - 2G P3(A;, ^^A^- A^^^;\j^+ A;^^, , P3+ A^ ^^-^) and where the replace irent of the functions of space ^, \, 9, is \li = z ' p-|^ + e q2, A = e p2 f ai^d 6 = q-|^ + /r P2' We now start the construction of the lowest order magnetic rrontnt adiabatic invariant.

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