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Automation of the guiding center expansion
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20.For some quick intuition regarding this ansatz, recall that the time-advance map associated to an arbitrary vector field is given by . Thus, given is found by sequentially flowing along the vector fields for −1 unit of time each, starting from x.
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24.Demanding the transformed to be gyrosymmetric is equivalent to demanding that the transformed to be equal to the sum of a gyrosymmetric one-form and an arbitrary closed one-form. This follows from the fact that is left unchanged upon replacing with for an arbitrary closed one-form , i.e., .
25.F stands for “fibered.”
26.ND stands for “non-degenerate.”
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