## 1. Introduction

[2] At short perpendicular spatial scale, parallel electric fields and large wave Poynting flux in dispersive shear Alfvén waves are speculated to produce electron acceleration up to the keV range [*Chaston et al.*, 2003]. There is strong observational evidence for this in the case of short parallel wavelength inertial or kinetic scale Alfvén waves propagating on the PSBL [*Keiling et al.*, 2001; *Wygant et al.*, 2002] and polar cusp [*Su et al.*, 2001]. It is also known that low frequency (long parallel wavelength) Pc5-range shear Alfvén waves are associated with modulations of the optical aurora [*Samson et al.*, 1991]. This is suggestive of a common mechanism for electron acceleration operating in SAWs over a wide range of wave phase velocities. However, an important question is whether the precipitation observed under short perpendicular scale Pc-5 field line resonances is produced by the wave itself. While we cannot provide closure on this issue, we consider this particular aspect in this paper.

[3] Many authors have considered mechanisms that are speculated to produce parallel electric fields of large enough magnitude to explain electron acceleration by dispersive Alfvén waves [*Wei et al.*, 1994; *Lu et al.*, 2003]. The existence of a parallel electric field is clearly not sufficient, as explaining electron acceleration involves understanding the response of the electron distribution function to the wave [*Hui and Seyler*, 1992; *Thomson and Lysak*, 1996; *Kletzing and Hu*, 2001; *Watt et al.*, 2005], and vice versa. If the wave phase velocity is comparable to the electron thermal speed, linear Landau damping can be expected on the finite slope of the electron velocity distribution function. Electrons moving slower than the wave gradually pick up energy from the wave as they surf on wave phase fronts, whereas those electrons moving faster than the wave will lose energy. A net energy gain for electrons is therefore expected when the distribution function has a negative velocity gradient at the wave phase velocity. On the other hand, at long parallel wavelengths characteristic of low frequency Pc-5 field line resonances, the wave phase velocity can be much smaller than the thermal speed over a significant extent of geomagnetic field lines, implying that electrons in linear Landau resonance with the wave are in the part of the distribution function that has essentially zero slope. In this case, the net energy gain of the electrons will be essentially zero. This simple conceptual framework neglects, however, nonlinear trapping of electrons in the wave, and the effect of the wave on current carrying electrons at both high and low altitude.

[4] In cold plasma with *ω*/*k*_{∥} ∼ ν_{A} > ν_{th} field-aligned electron currents in long period Pc-5 waves strongly perturb electron orbits. The distribution function must shift appreciably in velocity space to accommodate the wave current. This implies an increase in the number of electrons moving at or near the wave phase velocity. The nonlinear interaction of waves and particles thus offers the possibility of producing beams of accelerated electrons. In reality, long-period field line resonances [*Chen and Hasegawa*, 1974; *Southwood*, 1974; *Kivelson and Southwood*, 1986] are on geomagnetic field lines that encompass field-aligned variations in temperature, magnetic field strength and density, particularly at low altitude below ∼1–2 *R*_{E}. Geomagnetic field line convergence also implies a varying perpendicular scale of the wave. In spite of this complexity, it is nevertheless useful to investigate self-consistent nonlinear wave-particle interactions in field line resonances, in order to test some basic concepts. In the material that follows, we present Vlasov drift-kinetic modeling of plasma having a fixed temperature, density and magnetic field strength. These restrictions may seem severe, but nevertheless they reveal some interesting and informative aspects of wave-particle interactions that can be tested in more complete models.