The chaotic single particle orbits in the geomagnetic tail are used to calculate the collisionless conductivity. It is shown that the stochasticity from inhomogeneous magnetic fields leads to a power law decay of the single particle correlation function similar to an elastic collisional process. The height-integrated dissipative part of the collisionless conductivity governs the irreversible stochastic heating of the plasma sheet. Both exponentially growing reconnection type magnetic perturbations and a sinusoidal pulse with a half period up to 1 hour in duration are used to analyze the plasma sheet heating. ¿American Geophysical Union 1991