| Paper | Title | Page |
|---|---|---|
TUPSA11 |
Longitudinal Dynamics of a Bunch of Charged Particles in a Traveling Wave Field | |
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| The longitudinal dynamics of a bunch of charged particles in a traveling wave field has been studied. A Lagrange function for this motion is constructed and the Lagrange equation describing longitudinal envelopes of the bunch is derived. The obtained equation describes longitudinal envelopes of a bunch of charged particles. It is advantageous to the well-known equations of envelopes, primarily, in being simple. Additional advantages are as follows. First, the solutions of equation determine not only the longitudinal size of a bunch, but also the width of its energy spectrum. Second, the equation has been derived without any restrictions imposed on the bunch length (phase space dimension), so that the model is nonlinear and, hence, more general. Third, the equation takes into account the acceleration of a bunch. Finally, Lagrange equation takes into account the force of the intrinsic Coulomb field of a bunch in terms of the naturally included ellipsoid model, so that this envelope equation is self-consistent. | ||