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About Simulation K.Ohmi

About Simulation K.Ohmi. Simulation is very different from cases, lepton machine (beam size is very small compare than chamber) and proton beam (similar size).

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About Simulation K.Ohmi

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  1. About Simulation K.Ohmi • Simulation is very different from cases, lepton machine (beam size is very small compare than chamber) and proton beam (similar size). • The self consistent simulation, multibunch passage, cloud generation, single bunch instability of each bunch are solved simultaneously. • The coupled bunch instability must be treated self-consistently as is already done. • In my impression this type self-consistent simulation of single bunch instability with multibunch beam is only possible in linac like HIF . • I would like to know reliable method for ring accelerators with self-consistency. • Now we decide cloud density first and then study interactions with cloud with the density localized near beam. For proton beam, since the size is comparable with the chamber, boundary condition and whole electron cloud can be treated. • It is important to spend resources to include lattice information to study incoherent effects.

  2. Simulation technique • Potential kick & transfer map, so-called second order integrator, is used to guarantee the symplecticity, • The potential f(x,y,z) is solved by PIC method. • Solver: uniform mesh (FFT, FACR), nonuniform mesh

  3. Coherent effect (Fast head-tail) • Interactions in a synchrotron period is treated smoothly. • One interaction in a revolution is enough basically if the betatron tune is far from sychrotron tune + tune shift. • The computation results should scale re/ns, or saturate for increasing interaction point.

  4. Simulation of incoherent emittance growth • Beam interacts to cloud with various size (maybe scale to beam size, beta function) at positions of beta function and betatron phase. • Whole nonlinear interaction is integration of m-th nonlinear component times bm/2 and its betatron phase factor. • Uniform beta and uniform betatron phase advance give an excitation of unphysical structure resonance or unphysical resonance suppression.

  5. Importance of Lattice • Nonlinearity of beam-cloud interaction • Integrated the nonlinear terms with multiplying b function and cos (sin) of phase difference F: linear transformation f: cloud interaction Nonlinear term should be evaluated with considering the beta function and phase of position where electron cloud exists. Unphysical cancel of nonlinear term may be caused by simple increase of interaction point.

  6. OCS • Integrate every 2 m, • Bend B=0.2T, other drift. • Phase advance with 2np is integrated and whole lattice is matched at the end of arc cell.

  7. Model of lattice 2p cell f f f f f f f Other part: F1 Since f is symmetric for x-y, p cell is possible.

  8. Growth and bunch profile • Electron cloud is assumed to distribute along the arc cell. • rth=6.8x1010 m-3, the half of previous simulation.

  9. Electron is assumed to distribute only in bending magnets. (B=0.2T) • The threshold is again rth=6.x1010 m-3 Coherent instability Incoherent growth

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