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tokens: to the shortening of the flux tube or slingshot effect of the collapsing field (i.e., the Fermi acceleration of type A or B; Northrop 1963 ), causing an increase in the parallel energy. However, Figure 5 (a) demonstrates that this is only the case for small pitch angles. However, these orbits are reflected at the bottom boundary ( z = 0). This assumption is presumably unrealistic, as discussed in Section 9 . It is also noteworthy that none of the orbits illustrated in Figure 4 have come close enough to the generalized x -line or the separator to have crossed the presumed region of the parallel electric field (within the estimated ion inertial length or resistive scale). Thus, pre-acceleration by the direct electric field is probably not an important factor unless this region were greatly extended, for instance, through turbulent effects. The stepwise energy gain, as illustrated in Figure 5 , can be interpreted in two ways. This becomes obvious from the energy equations (see Giuliani et al. 2005 ; Grady et al. 2012 ), which, for simplicity, we write in its nonrelativistic form, which is derived from Equations ( 7 ) and ( 8 ) with neglect of the inertia term The parallel electric field term is included in Equation ( 28 ) for completeness; although, it is disregarded in our orbit calculations, as discussed in Section 3.4 . The first and last terms on the rhs of Equation ( 27 ) describe the betatron effect from the increasing (or decreasing) magnetic field strength or the drift motion into the spatially increasing (or decreasing) magnetic field. Similarly, the last term in Equation ( 28 ) describes the gain (or loss) from the motion in a curved field, which is the first-order Fermi acceleration (type B; Northrop 1963 ). However, these last terms can also be re-written as where and are the gradient and curvature drifts, as defined in Equation ( 7 ). Thus, the betatron and Fermi acceleration of the electrons in the collapsing field are equivalent to the gradient B and curvature drift components, respectively, antiparallel to the electric field (see, Northrop 1963 ; Birn et al. 2013 ). These terms dominate the acceleration. It occurs at the loop tops because both the drift and the field gradients are largest there. 6. Parameter Effects Choosing the high-shear, initially force-free case as an example, we have explored the influence of various parameters on the amount and location of particle acceleration. Figure 6 provides a comparison of the flux enhancements for t = 110 at z = 1, which is slightly above the photospheric boundary, for different energies, pitch angles, and relativistic parameters ξ (representing the ratio of the characteristic energy to the electron rest energy). Panels (a)–(d) of Figure 6 show the relative energy gains, as a proxy of the flux enhancement, for different parameters indicated in the margin, while panels (e)–(g) show MHD quantities that might be related to the energetic particle fluxes: downward Poynting flux S z ,