JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 96, NO. A5, PAGES 7931-7932, MAY 1, 1991 Reply S. QIAN Centerfor Nonlinear Studies,Los A!amos National Laboratory, Los A!amos, New Mexico M. K. HUDSON Physicsand AstronomyDepartment, Dartmouth College, Hanover, New Hampshire I. ROTH Space SciencesLaboratory, University of California, Berkeley The point raised by Omura [this issue] in his comment is well taken, and we have computed power spectra of the relevant quantities in our simulations to test the mechanism proposed by Omura et al. [1988] for parallel ion heating by electromagnetic ion cyclotron (EMIC) waves as it appliesto the simulations of Omura et al. [1985]and Qian et al. [1990]. The power spectra shown in Figure 1 were computed at a fixed point in space over the time interval 600-100011-1, inverse units of the hydrogen gyrofrequency, during the saturationphase of the instability, for the parametersof run II described by Qian et al. in their Figure 4. Figure l a is a plot of by, the perpendicular wavemagnetic field,andone sees a peak at the mode frequency which is driven linearly unstable by the hydrogen loss cone around •o = 0.1511. Figure lb shows a power spectrum plot of ex, the parallel electric field component,for the same point in space, time period, and parameters as Figure l a. One sees a dominant peak at zero frequency, which supports the mechanism proposed by Omura et al. [1985, 1988] subsequent to their original simulations.At a lower amplitude one may observe components at frequencies0.2, 0.374, and 0.6411.Figure lc showsa plot of the corresponding power spectrum for vx averagedover one cell VA/11, where VA is the hydrogen Alfv6n speed. One observesa shift to finite frequency which persists when one examines contour plots in frequency- wave number spacefor vx, taken over the whole system. Figure 2 shows the contour plots in frequency-wave number space of by and e x, averaged over thetimes 256 < t11 < 512 (Figures 2a and 2b) and 512 < t11 <1024 (Figures 2c and 2d). We observe the main power of the magnetic fluctuationsaround •o --• 0.1511and the main power of the electric fluctuations around •o = 0, with smaller amplitudes in the region 0.2 < •o/11 < 0.3 at earlier times. We agree that the trapping mechanism by a stationary electrostatic potential has the most significantcontribution to the parallel heating of cold ions. This heating involves sloshing of ions in an effective stationary potential well which is proportional to the perturbed magnetic field. The increase in the perturbed magnetic field increases the effec- tive potential. This heating mechanism is different from acceleration by a wave with a finite phase velocity. Addi- Copyright 1991 by the American GeophysicalUnion. Paper number 91JA00050. 0148-0227/91/91J A-00050502.00 DI2 by .o08 .oo4 .00060 ex D0020 2.O (a) øo I.O 2.0 (b) .0060 (c) Vx .0040 DO20 øo ID 2D co/ Fig. 1. Fourier components of (a) by, the perpendicular mag- netic field, (b) ex, the parallel electric field, and (c) Vx, the spatially averaged ion velocity, as a function of frequency, averaged over the times 600 < tlln < 1000. 7931