# An exponential integrator for the drift-kinetic model

## TL;DR

This paper introduces an exponential integrator for the drift-kinetic equation that removes the CFL constraint, conserves mass, reduces computational effort, and performs efficiently in plasma instability simulations.

## Contribution

The paper presents a novel exponential integrator for the drift-kinetic model that improves efficiency, conservation, and allows higher order methods, outperforming traditional splitting approaches.

## Key findings

- Removes CFL constraint in simulations
- Achieves mass conservation up to machine precision
- Enables larger time steps comparable to existing methods

## Abstract

We propose an exponential integrator for the drift-kinetic equation in cylindrical geometry. This approach removes the CFL condition from the linear part of the system (which is often the most stringent requirement in practice) and treats the remainder explicitly using Arakawa's finite difference scheme. The present approach is mass conservative, up to machine precision, and significantly reduces the computational effort per time step. In addition, we demonstrate the efficiency of our method by performing numerical simulations in the context of the ion temperature gradient instability. In particular, we find that our numerical method can take time steps comparable to what has been reported in the literature for the (predominantly used) splitting approach. In addition, the proposed numerical method has significant advantages with respect to conservation of energy and efficient higher order methods can be obtained easily. We demonstrate this by investigating the performance of a fourth order implementation.