On energy loss of narrow and dense ultrarelativistic bunch in plasma

Energy balance of a particle bunch propagating through the plasma is considered for the bunches of a high density (compared to plasma) and a small radius (compared to anomalous skin depth). Energy loss to scattering of near-axis plasma electrons is estimated. This component of energy balance is shown to be important but not excessively high for the parameters interesting for high energy physics. In particular, the energy loss to near-axis electrons is proved to remain finite as the bunch radius tends to zero