Einzel lens and Momentum Modulation

What happened in DA's beam commissioning

1. Einzel lens is adopted to chop the beam (several us out of 5ms): using Marx generator with a pulse profile.
2. This technique has a byproduct that momentum modulation would occur to the rise and fall region of that pulse for Einzel lens.
3. The momentum modulation in the beam head and tail has two effect: 
1. good one: compensate somehow to the longitudinal space charge effect
2. bad one: resulting micro-bunching inside the beam

remained issues:

1. explain why the pulse used for Einzel lens results in momentum modulation in rise and fall region(beam head and tail)
2. could you give a mathematical description of that process, along with related parameters, e.g. rise&fall time, dimension of einzel lens, operation voltage(for 14 kv, 17 kv ->11 kv, for 10kv, 13->8kv)
3. what do you mean by "compensate", could you give some example?
4. could you give a mathematical description on the effect of momentum modulation within the beam? Especially, what's the difference between motions with and without space charge? Is there still micro-bunching structure inside the beam without space charge?