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Beam Energy Spread and Longitudinal Emittance in a RF gun Z. Huang

Beam Energy Spread and Longitudinal Emittance in a RF gun Z. Huang P. Emma, C. Limborg, G. Stupakov, J. Wu SLAC (LCLS week, April. 5, 2005). Local energy spread for a photoinjector beam. LCLS gun simulation at 1 nC. TTF gun measurement at 4 nC. M. Hüning, H. Schlarb, PAC’03. 3 keV rms.

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Beam Energy Spread and Longitudinal Emittance in a RF gun Z. Huang

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  1. Beam Energy Spread and Longitudinal Emittance in a RF gun Z. Huang P. Emma, C. Limborg, G. Stupakov, J. Wu SLAC (LCLS week, April. 5, 2005)

  2. Local energy spread for a photoinjector beam LCLS gun simulation at 1 nC TTF gun measurement at 4 nC M. Hüning,H. Schlarb, PAC’03. 3 keV rms DE/E simulation measured Dt (sec) • 3~4 keV is too small to be useful for a SASE FEL • LCLS uses a laser heater to increase it to 40 keV to suppress the microbunching instability in the accelerator

  3. Linac tunnel LCLS laser heater ‘Laser Heater’ DL1 Gun S1 S2 L0-2 24 MV/m L0-1 19.8MV/m Example: final long. phase space at 14 GeV for initial 8% uv laser intensity modulation at initial =150 m E/E 110-4 210-3 t (sec) t (sec) no laser heater with laser heater

  4. Introduction • While LCLS increases beam local energy spread, some other beam manipulation schemes may require a tiny energy spread (emittance exchange, tunable HGHG) • Need a general understanding of the local energy spread and longitudinal phase space in a RF gun • Energy gain (loss) due to RF and space charge effects can depend on transverse coordinates (r), both of which contribute to the local energy spread • We compare analytical calculations with simulations as well as experimental results from GTF and TTF

  5. RF effect • Energy gain of a particle with v = c through a round accelerating structure is independent of transverse offsets • In a RF gun, this theorem (related to P-W) is violated • electron starts from rest (v ≈ 0) • field starts with a half-cell • r-dependent energy gain is small due to rapid acceleration • We use latest RF gun field • Integrating single particle equation of motion yields • E ≈1 keV at gun exit for an electron at r0=1 mm relative to on-axis acceleration E E

  6. Discussions • D. Dowell et al. (EPAC2004) reports E = 2.7 keV at r0 = 1 mm for the RF field of an older LCLS gun design • It is still small on the absolute scale, but nearly three times larger than the latest RF gun field, what causes the change? • However, Averaging over the whole bunch, E ~ 1 keV or less due to RF effect, a small contribution to the local energy spread unless bunch charge is extremely low

  7. Space charge effect • At higher charge or current, space charge important. Longitudinal space charge field can have r dependence • As a simple estimation, we take pencil beam approximation (beam radius rb < lz, lz fwhm bunch length) LCLS bunch rb = 1 mm, lz = 3 mm (subtlety near cathode) • LSC field in a beam pipe of radius a is • Assuming linear acceleration from rest to f over distance L  space charge induced energy change is

  8. Space charge induced energy spread • r independent terms contribute to correlated energy spread • r dependent term contributes to uncorrelated (local) energy spread • Average over whole bunch, take dI/dz ≈ I0/(2z) • For LCLS gun at 1 nC with a 10 ps fwhm bunch length, • I0 = 100 A, f = 11, L = 10 cm, z = 1.2 mm • <E> ≈ 3.3 keV For TTF experiment at 4 nC but with z = 3.54 mm, take (f/L)L-band = 1/3 (f/L)S-band • <E> ≈ 4.5 keV

  9. Comparison with GTF • Compare with D. Dowell et al., NIMA 507(2003) p331, using measured charge and rms bunch length, 15 pC data is excluded due to resolution limit measurement theory • Yet to be compared with longitudinal tomography data (H. Loos et al., NIMA 528 (2004)

  10. Longitudinal Emittance • Longitudinal emittance determined by space charge is G=f/L is the effective acceleration gradient • Comparison with GTF results of D. Dowell et al. measurement theory

  11. Summary • RF effect to the local energy spread is small, although some unresolved difference between old and new RF gun fields • For decent bunch charge and current, space charge induced local energy spread is the dominant contribution • Analytical estimations are in consistent with simulations and experiments. The small local energy spread requires beam heating to suppress microbunching instability • Longitudinal emittance due to space charge only depends on bunch current and acceleration gradient in a RF gun

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