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Particle-in-cell (PIC) simulations are widely used as a tool to investigateinstabilities that develop between a collisionless plasma and beams of chargedparticles. However, even on contemporary supercomputers, it is not alwayspossible to resolve the ion dynamics in more than one spatial dimension withsuch simulations. The ion mass is thus reduced below 1836 electron masses,which can affect the plasma dynamics during the initial exponential growthphase of the instability and during the subsequent nonlinear saturation. Thegoal of this article is to assess how far the electron to ion mass ratio can beincreased, without changing qualitatively the physics. It is first demonstratedthat there can be no exact similarity law, which balances a change of the massratio with that of another plasma parameter, leaving the physics unchanged.Restricting then the analysis to the linear phase, a criterion allowing todefine a maximum ratio is explicated in terms of the hierarchy of the linearunstable modes. The criterion is applied to the case of a relativistic electronbeam crossing an unmagnetized electron-ion plasma.

How large can the electron to proton mass ratio be in Particle-In-Cell simulations of unstable systems?