Effect of numerical noise on beam emittance growth in PIC code

In particle-in-cell (PIC) simulation, errors in space charge forces are of random character. It results in an unphysical increase of effective beam emittance, even while a symplectic integrator is used. To establish a quantitative measure of this effect on beam dynamics, an analytical model of an equilibrium beam affected by random errors in space charge field calculations is considered. An explicit expression connecting beam emittance growth with beam brightness, integration step and the value of the random error in the space charge field is discussed