Magnetic Compression of High Brightness Beams: Survey of Experimental Results Scott G. Anderson ICFA Sardinia July 2002

July 2, 2002S. G. Anderson - ICFA Sardinia2 Magnetic Compression Motivation — increase brightness, need sub-ps bunches Problems — 6D phase space deterioration caused by collective effects –Acceleration fields – Coherent Synchrotron Radiation (CSR) –Velocity fields – Space-charge Experiments –CTF, TTF, SDL, APS, UCLA, … –Features of the data Phase space dilution – emittance growth, momentum spectrum filamentationPhase space filamentation – both longitudinal and transverse –Comparisons with theory/simulation Simulations reproduce rms quantities, but not intricate phase space structures seen in expt.

July 2, 2002S. G. Anderson - ICFA Sardinia3 Operating Principle of Magnetic Compression Acceleration ahead of crest of rf wave + chicane dipoles acts as lens + drift. accelerating wave

July 2, 2002S. G. Anderson - ICFA Sardinia4 CTF II Emittance Measurements* Large bend plane emittance growth observed as a function of compression Only CSR and/or space- charge were reasonable sources of  PARMELA predicts 10% of measured  CSR-TRACK predicts 60% of measured  *from: H. H. Braun, et al., Phys. Rev. Lett. 84, 658 (2000).

July 2, 2002S. G. Anderson - ICFA Sardinia5 CTF II Emittance and Momentum Distribution Measurements* *from: H. H. Braun, et al., Phys. Rev. ST Accel. Beams 3, (2000).

July 2, 2002S. G. Anderson - ICFA Sardinia6 CTF II Emittance versus Horizontal Size

July 2, 2002S. G. Anderson - ICFA Sardinia7 TTF

July 2, 2002S. G. Anderson - ICFA Sardinia8 TTF

July 2, 2002S. G. Anderson - ICFA Sardinia9 SDL Current (A) Time (ps) Current (A) Time (ps) Current (A) Time (ps) RF zero phasing measurement of electron beam time profile. No compression Mild compression Strong compression Strong micro-bunching with compression — source not agreed upon.

July 2, 2002S. G. Anderson - ICFA Sardinia10 APS?

July 2, 2002S. G. Anderson - ICFA Sardinia11 UCLA Experiment Lower energy (< 12 MeV) — space-charge may play significant role in compression This allows/requires emittance measurement using slits: Transverse phase space is directly measured

July 2, 2002S. G. Anderson - ICFA Sardinia12 Interferometer Data Delay Arm Position Normalized Signal

July 2, 2002S. G. Anderson - ICFA Sardinia13 Emittance Versus PWT Phase Sharp increase is a consistent feature in data

July 2, 2002S. G. Anderson - ICFA Sardinia14 Bifurcation of Transverse Phase Space  z = 4 ps  z = 0.6 ps

July 2, 2002S. G. Anderson - ICFA Sardinia15 Varying Phase or Field Pulse Length [psec] Emittance [mm mrad] Emittance growth and phase space structure is a function of compression.

July 2, 2002S. G. Anderson - ICFA Sardinia16 Emittance Growth Vs Beam Size  x [mm] Emittance Growth [mm mrad]

July 2, 2002S. G. Anderson - ICFA Sardinia17 Simulation Different codes model different processes (acceleration fields versus velocity fields.) Codes employed: –TREDI: Solves Lienard-Wiechert potentials. –PARMELA: Provides input distributions for TREDI. Point- to-point space charge for comparison. –ELEGANT: CSR only calculation. Simulations indicate that for this experiment, acceleration fields do not contribute much emittance growth, the space charge fields are the dominant effect.

July 2, 2002S. G. Anderson - ICFA Sardinia18 Simulation Simulation is difficult. Number of macro-particles is low because of time-intensive space-charge calculations. Sharp emittance increase when bifurcation begins is missing in simulations. Emittance [mm mrad] PWT Phase [deg.]

July 2, 2002S. G. Anderson - ICFA Sardinia19 Heuristic Model To analyze the effect of space-charge in the compressor, we model the beam as a series of longitudinal slices. Since the beam energy spread is heavily correlated to slice position, we assume that there is no energy spread (no dispersion) within a single slice. Space-charge forces push a slice based on the fields at it’s centroid due to the other slices. Use standard envelope equations to evolve the sizes of single slices.

July 2, 2002S. G. Anderson - ICFA Sardinia20 Configuration Space ‘gymnastics’ in the Model Configuration SpaceLong. Phase Space Beam “folds over” in configuration space. (no space-charge)

July 2, 2002S. G. Anderson - ICFA Sardinia21 Space-charge in the model In simple model integrate  space- charge force in last magnet to get  x’ between slices Model predicts size dependence In simulation use 3D ellipsoidal fields ellipsoid edge Cartoon of config. space evolution.

July 2, 2002S. G. Anderson - ICFA Sardinia22 Simple calculation with the model Emittance [mm mrad] x’ [mrad] s/R 00 Kick applied between two slices in the last magnet.

July 2, 2002S. G. Anderson - ICFA Sardinia23 Slice Model Simulation Trace space bifurcation Configuration space Input size dependence

July 2, 2002S. G. Anderson - ICFA Sardinia24 Bifurcation in PARMELA z phase space Energy distributionConfig. space

July 2, 2002S. G. Anderson - ICFA Sardinia25 Summary of UCLA Experiment Features of the data: –Trace space bifurcation –Emittance growth inversely proportional to beam size Simulation shows that space-charge is the dominant effect Slice model simulation, and PARMELA/TREDI simulations show same features as data, but not as pronounced. Possible pre-existing structure in phase space and/or CSR combines with space- charge effects to accentuate behavior seen in data. Blue statements seem applicable to other experimental data as well!