  The standard particle-in-cell algorithm suffers from grid heating. There
exists a gridless alternative which bypasses the deposition step and calculates
each Fourier mode of the charge density directly from the particle positions.
We show that a gridless method can be computed efficiently through the use of
an Unequally Spaced Fast Fourier Transform (USFFT) algorithm. After a spectral
field solve, the forces on the particles are calculated via the inverse USFFT
(a rapid solution of an approximate linear system). We provide one and two
dimensional implementations of this algorithm with an asymptotic runtime of
$O(N_p + N_m^D \log N_m^D)$ for each iteration, identical to the standard PIC
algorithm (where $N_p$ is the number of particles and $N_m$ is the number of
Fourier modes, and $D$ is the spatial dimensionality of the problem) We
demonstrate superior energy conservation and reduced noise, as well as
convergence of the energy conservation at small time steps.
