Space Charge Correction on Emittance Measurement of Low

Space Charge Correction on Emittance Measurement of Low Energy Electron Beams Colleen Treado Cecile Limborg-Deprey SULI 2011 August 11, 2011

Phase Space Charged particle beam in 6 D: • • -- spatial coordinates -- conjugate coordinates • Normalized momenta (d/ds) along beam trajectory Emittance represents volume of beam in phase space 2 SLAC-SULI 2011 Presentations SLAC, Menlo Park, CA, 8/11/11

Phase Space • RMS phase space ellipse ; • Courant-Snyder (Twiss) parameters describe orientation and shape C. K. Allen, “S Liouville’s Theorem: • • Emittance conserved throughout beam transport Beam described entirely by second order moments 3 SLAC-SULI 2011 Presentations SLAC, Menlo Park, CA, 8/11/11

Linear Beam Dynamics • Evolution of trajectory of charged particle beam under linear components of Lorentz forces: • Drift spaces and electromagnets • Quadrupoles act like optical lenses – focus in one plane, defocus in other defocusing quadrupole drift space Focusing quadrupole 4 SLAC-SULI 2011 Presentations SLAC, Menlo Park, CA, 8/11/11

Transfer Matrix Approach Harmonic oscillator – dependent on beam element Transfer matrices represent linear components of forces of beam transport elements. 5 SLAC-SULI 2011 Presentations SLAC, Menlo Park, CA, 8/11/11

Particles vs. Ensemble Transport 6 SLAC-SULI 2011 Presentations SLAC, Menlo Park, CA, 8/11/11

Space Charge • Electric forces between charged particles generate self-fields that defocus beam • Non-negligible in beams of low energy, high charge, and/or short bunch length – magnetic forces do not balance electric 7 SLAC-SULI 2011 Presentations SLAC, Menlo Park, CA, 8/11/11

Transport Code • Discretize beam – quadrupoles and drift spaces • Transport beam over small subsections, Δs, using transfer matrices • Apply space charge kick with space charge matrix • Model entire beam transfer through product of individual beam transfer matrices, including space charge 8 SLAC-SULI 2011 Presentations SLAC, Menlo Park, CA, 8/11/11

Probing Phase Space Measure observable, <x 2>; can’t measure x’ directly X Q X 0 9 SLAC-SULI 2011 Presentations SLAC, Menlo Park, CA, 8/11/11

ASTRA Simulations Simulation of 100 Me. V Beam with Space Charge 10 Quadrupole Scan of 100 Me. V Beam SLAC-SULI 2011 Presentations SLAC, Menlo Park, CA, 8/11/11

Transport Code Results 11 SLAC-SULI 2011 Presentations SLAC, Menlo Park, CA, 8/11/11

Conclusions and Future Work • Inclusion of space charge necessary in calculation of correct emittance of lower energy beams ( < 100 Me. V ) Solve: • Form factor • More work necessary for very low energies 12 SLAC-SULI 2011 Presentations SLAC, Menlo Park, CA, 8/11/11