Low Emittance Electron Injectors

Transcription

1 Low Emittance Electron Injectors Chuanxiang Tang Accelerator Lab., Dept. of Engineering Physics, Tsinghua University Beijing OCPA Accelerator School, Yangzhou, August 3rd, 2006

2 Content 1 Introduction to electron guns 2 Photocathode rf gun 3 Emittance evolution in electron injectors

3 1.1 Why low emittance electron injectors needed? XFEL LC Luminosity η L P δ γ σ RF RF BS z 3/ 2 Ecm ε n, y β y ηrf P E cm RF δ ε BS n, y σ z β y Gain Length Thomson or Compton Scattering Wavelength Requirement ε < λs 4π ε n =βγε Brightness

4 1.2 Some Basic Concepts of Emittance Concept: Emittance is used to describe the super-volume in the 6-dimentional phase space, as coordinates (q1,q2,q3) and momenta(p1,p2,p3) in Cartesian coordinate systems. If the particles inside any closed surface s(t) in the phase space, surfer only conservative forces, the volume v(t) enclosed by the surface s(t) will be invariant with time. Emittance is the volume v(t) occupied by the particles of a bunch. Without coupling between q1,q2,q3 Phase space: (q1, p1), (q2, p2), (q3, p3) Emittance is a area of the phase space

5 RMS RMS Normal Emittance Accelerator Lab of Tsinghua University RMS Emittance ε n = π mc e x 2 p 2 x x p 2 x Here m e c means that p x =β x γ. In most case, ε n is expressed in π.m e c.μm RMS Geometrical Emittance ε = π x x x x x =p x /p z =β x /β z is the divergence angle, and ε is expressed in π.mm.mrad Other expressions of RMS Emittance ε n = 4 π mc e x px x px ε = 4 π x x x x What s difference between them? Assume all the particles have same P z ε n = βγ ε

6 RMS Emittance A gaussian phase-space distribution may be specified as: p x x And To simplify the analysis, let,and rms normal emittance is x px ψ ( x, px ) = exp[ ( + )] 2 2 2π x p x px x xp x 2 = 0 x px 2 And Consider an ellipse + = K 2 2 in (x, p x px x ) space defined by: AK ( ) = π mc e K x p The area of this ellipse is: The fraction of the bunch within this ellipse is readily computed: x For K=l, t,he ellipse has an area equal to the normalized RMS emittance, and contains 39.35% of the part,icles. The maximum x coordinate of the ellipse is the RMS value of x, while the maximum p x coordinate of the ellipse is the RMS value of p x. For K=2, the ellipse has an area equal to four times the normalized RMS emittance, and contains 86.47% of the *M.Borland,A High-Brightness Thermionic Microwave Electron Gun, SLAC-402(1991),Ph.D.Thesis ε 2 2 n = π mc e x px p x x

7 x RMS Emittance and Electron Beam The transverse momentum p x & the divergence angle x The RMS geometrical emittance will decrease with the particales being accelerated, but the RMS normal emittance will remain the same. p x dx dx dz px = mvx = m = m = mvz x = pz x dt dz dt dx x = = tan( θ ) θ dz x x x x θ dz 10MeV 40MeV v dx z z x x x x x x x x x x

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9 Photo-electric emission: 1)photo-current is proportional to photon number (if photon energy not changed) 2)The maximum kinetic energy of the photo-electron is proportional to photon energy Metal: Mg 0.4%, Cu 0.05% Semiconductor: alkali-based Na2KSb:Cs, K2CsSb, Cs2Te 266nm 6%~12%, 251nm 16% GaAs 2.55eV(486nm) 14% GaAs:Cs 2.3eV 0.26%

10 Secondary emission: When the primary electron hits the cathode, atoms will be shocked strongly. Some electrons can cross the potential well and become secondary electrons. min( R( E ), d) 0 B d E( x) α x δr( E0) = e dx ε dx 0

11 1.4 Electron Guns DC Gun: Triode structure: Cathode, anode, and grid electrode to control the emission. Wehnelt electrode for the collimated space charge flux. The pulse length is limited down to ~1ns due to the switching speed of the driver circuit. The bunch length is more than 1ns. This long pulse can be considered to be a continuous beam, in which the gun is operated in the space charge limit.

12 From Timothy J. Waldron s Presentation, Functional Requirements for IMRT

13 Field Emission Gun From Arno Erol Candel, Ph.D. Thesis, 2005

14 Multipactor Gun SE Yield of Diamond Electron Energy (kev) SEEP Capsule (Ben-Zvi 06)

15 B n I p = 2 ε ε nx ny Thermionic RF Gun Accelerator Lab of Tsinghua University High brightness Simple Alpha magnet needed to compress the bunch length and serve as a momentum filter Electron back bombardment effect Pulse length: cathode damage and beam loading Repeat rate: cathode damage Energy spread: beam loading Emittance : low electric field at cathode B n I p = 2 ε ε nx ny I Cathode support Coupling Hole t1 t2 Im I Im/2 t Symmetry hole ΔΕa t2 ΔΕ t1 W e From Chuanxiang tang s PhD thesis, 1996

16 Coil Poles Beam Line N S

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18 n Accelerator Lab of Tsinghua University Emittance in Photoinjectors ε ~ ε th + ε sc + ε rf + ε mp + ε Bz 2ηε scε rf ε th ε sc ε rf ε mp ε Bz η Initial Emittace or Thermal Emittance Space Charge Emittance RF Emittance Multi-pole mode of RF field caused Emittance Emittance because of Magnetic field Bz at cathode surface Coupling between space charge effect and RF effect Mainly From : K. J. Kim. RF and Space Charge Effects in Laser-Driven RF Electron Guns[J]. Nuclear Instruments and Methods in physics research section A. 1989, 275:201

19 Emittance Consideration in a Photoinjector RF cavity optimization Electric field gradient Cathode: material and its surface Bunch charge and its shape Laser pulse (space and time) Coil design ( emittance compensation) Time jitter (time dependence electric field)

20 Energy to Laser Phase MV/m 97 MV/m 122 MV/m 146 MV/m 5 W out (MeV) Laser Phase (degree)

21 Emittance to Solenoid Strength cm 19cm 21cm 2 ε rms,n /mm mrad B

22 Emittance vs Bz and Laser radius

23 Emittance vs Bz and laser injection phase

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25 New RF Design of the LCLS Gun 15 MHz mode separation Dual Feed Racetrack shape The cell-to-cell iris : the radius of the iris increased and the disk thickness reduced The profile of the disk iris was modified from circular to elliptical to reduce the surface field. Z-coupling of RF feeds Laser port holes Probe holes

26 2.3 Electric Field and Emittance

27 *D. T. Palmer. The Next Generation Photoinjector[D]. Ph.D. thesis, Department of applied physics of Stanford university, 1998

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29 2.4 Thermal Emittance of Metal Photocathde The normal Emittance ε n, rms For flat photocathode surface = < x >< p x > < xp x m0c > 2 ε thermal, rms = x rms p rms, x m c 0 = x rms 2 m E 0 m c 0 kin, x *By He Xiaozhong, Tang Chuanxiang, et al, High Energy Physics and Nuclear Physics Vol.28,No.9,

30 E The statistic average kinetic energy of electron from surface 1, x [ hν Φ α βe( φ)] 6 kin + R hν φ The thermal emittance of an idea flat cathode : ε n, rms, flat = 2 2 3m c *He Xiaozhong, Tang Chuanxiang, et al, High Energy Physics and Nuclear Physics Vol.28,No.9, *J. F. Schmerge, J. M. Castro, J. E. Clendenin, et al. Emittance and Quantum Efficiency Measurements from a 1.6 cell S- Band Photocathode RF Gun with Mg Cathode*[J]. SLAC-PUB

31 Compared with measured results *X. J. Wang, et al. Mg cathode and its thermal emittance[j]. LINAC *J. F. Schmerge, J. M. Castro, J. E. Clendenin, et al. Emittance and Quantum Efficiency Measurements from a 1.6 cell S-Band Photocathode RF Gun with Mg Cathode*[J]. SLAC-PUB *W. S. Graves, L. F. DiMauro, R. Heese, et al. Measurement of thermal emittance for a copper photocathode[j]. PAC

32 Thermal emittance of metal photo-cathode due to surface roughness The surface roughness causes the parallel kinetic energy increasing compared with the flat surface. If we assume that the parallel and the vertical kinetic energy of the electron emitted from the rough surface are equal,

33 The emittance caused by the electric field at the rough surface The stray electric field because of the microsurface*: Ele ctron m o- ving direction a x 1 -p -p/2 p/2 p Z X z = a cos( 2πx / p) * R. W. Klopfenstein, R. K. Wehner. The Electric Field Near Weakly Deformed Conducting Surfaces[J]. RCA Review. 1973, 34:

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35 Copper cathode (left) and Magnesium cathode (right) cut by diamond without polishing

36 Copper cathode (lower) and Magnesium cathode (upper) cut by diamond without (left) and with (right) polishing

37 Emittance caused by roughness

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42 Timing Jitter Measurement

43 2.6 Coil Bz at different current E E E-02 Bz at axis /Tesla E E E E-01 0A 10A 50A 100A 150A 180A E E-01 z /mm Bz(x=0,y=0) Bz(x,y)-Bz(0,0) /Tesla x0y0 x0y-4 x0y-2 x0y2 x0y z /mm Bz(x=0,y=-4,-2,0,2,4mm)-Bz(x=0,y=0)

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45 Evolution of the two kinds of emittance in a general photoinjector beamline One slice A ring in the slice Correlated slice Emittance Correlated Project Emittance

46 Correlated and Slice Emittances in Space Charge Dominated Photoinjectors* Slice Emittance: A transverse cross section of the beam is called a slice, and the emittance of a slice is called slice emittance. Slice emittance consists of two parts, one part is the thermal emittance and the other part is due to nonlinear space charge force. Correlated emittance: The growth of projected emittance is due in large part to the correlation between the phase space angle and the longitudinal position of slices. Normally, this part of projected emittance is called correlated emittance. Emittance compensation: Correlated emittance evolves as the beam propagates in the beamline, and can be eliminated at one or more specific points through selecting proper parameters of the beamline. This process of eliminating correlated emittance is called *He emittance Xiaozhong, Tang compensation. Chuanxiang, et al, to be published at NIM A

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48 Transverse Particle Motion Equation d ( p 2 r) = e ( E r βz cb θ ) = ee r( βz ) dt r ( ) 2 2 e λ ζ r 0 ( ζ, z) = πε 0β γ 0 ee γ r mc a r z ( ) r e 2 = e ( ) 2 4 πrn e b ζ, z 2 4πε 0mc k p = 2 3 βγ 1 1 r z k r r z 2 2 ( ζ, ) = 0( ζ ) 0 2 p ( ) kp0 ( ζ ) = kp( ζ, z = 0)

49 Slice Emittance and The Phase Space 1 r( ζ, z) = r + k ( ζ ) r z r ( ζ, z) = kp0( ζ ) r0z p0 0

50 After a thin lens at z=z l with focus of f 1 2 z 1 r( ζ, z) = r + k ( ζ ) r ( z+ z ) r + k ( ζ ) r z 4 f p0 0 l 0 p0 0 l 1 r0 1 r ( ζ, z) = k ( ζ ) r ( z+ z ) 1+ k ( ζ ) z 2 f p0 0 l p0 l

51 space charge dominated waist and ballistic waist (cross-over) x z Z space charge dominated waist - Strong space charge effect Laminar Current x z Z ballistic waist - Weak space charge effect Cross-over Current Carlsten, NIMA, 285, 313 (1989).

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53 Conditions of The Emittance Compensation for a Laminar Beam Emittance compensation means all of the slices are aligned in the phase space. If a thin lens is put at position z l, emittance compensation will happen at position z downstream from the lens. d dk 1 f 2 p0 = r = r z + z 0 l 2 2 z

54 Envelope Equation Linear model: space charge force, rf accelerating, external focus and initial emittance 2 ( ) 2 γ η γ ε r r eλ ζ σ r + σ r + σr = γ 8 γ σr γ σr Envelope evolution accelerating External focus and the rf focus Initial emittance Space charge Envelope is defined as:

55 Without Accelerating and Initial Emittance z r Coil at z l 2 (, z) k (, z) σ ζ + σ ζ = β r r λ ζ e 3 r γσ ( ) ( ζ, z) Brillouin Flow A particular solution is got when σ r =0: Perturbation around the Brillouin Flow : 2 ( ) ( ) ( ) ( ζ) e r β r 3 2 r γσeq σ eq ( ζ ) r λ ζ δσ ζ, z + k δσ ζ, z = δσ ζ, z = 1 e k β ( ) r λ ζ 3 γ δσr = σr σeq σeq ( ) 2 ( z) k ( z) δσ ζ, + 2 δσ ζ, = 0 r β r

56 Perturbation around Brillouin Flow Initial condition: r (,0) = σ r0 r ( ζ ) σ ζ σ,0 = 0 Solution: (, z) = ( ) cos( 2kβ z) (, z) = 2kβ 0 ( ) sin( 2kβz) σ ζ σ σ σ ζ r r r eq σ r ζ σr σeq ζ Oscillation frequency: 2k β Projected emittance and the emittance compensation

57 With Accelerating z Coil at z l A particular solution : σ γ η γ σ + σ + σ = 2 ( ) r λ ζ e r r r 3 γ 8 γ γ σr inv ( ζ, z) re λ( ζ ) ( 1 2) ( z) 2 = γ + η γ ( z) re λ( ζ ) ( 1+ 2) ( z) 1 σ inv ( ζ, z) = γ η γ Invariant Envelope inv ( ) ( ) = 2 γ σ ζ σ ζ γ inv is independent of ζ and z, which means the rates of slope for different slices and at different positions are same.

58 Perturbation around the Invariant Envelope γ 1+ η γ δσ r + δσ r + δσ r = 0 γ 4 γ 2 A particular solution ( z) ( ) cos 1+ η γ ln 2 γ 0 r = inv + r0 inv σ σ σ σ ( z) 1+ η γ 1+ η γ σ ( z) σ σ 2 γ 2 0 r = r inv sin ln ( ) ( ) 0 z γ ( z)

59 3.3 The evolution of the emittance The correlated projected emittance: The correlated slice emittance: *He Xiaozhong, Tang Chuanxiang, et al, A first-order analytical investigation on emittance evolution of relativistic sp dominated beams,nucl INSTRUM METH A 560 (2): MAY NIM A

60 Evolution of the two kinds of emittance in a drift tube beamline The evolution of the two kinds emittance in drift space can be depicted analytically as a function only of the propagating distance and several parameters determined by the initial phase space Initial parameter of the electron beam Kinetic Energy (MeV) 4.5 Transverse distribution uniform Hard edge Radius(mm) 4.7 Divergence at hard edge (mrad) -5.3 Longitudinal distribution flat top Pulse length (ps) 20 Current (A) 100 Initial energy spread 0 Initial emittance ε nr (z = 0)(μm) 12.0 (for project emittance) 4.0 (for slice emittance)

61 ' Δσ nr = 0 Correlated project emittance when Δσ nr =0, and Correlated slice emittance when Δr n =0,simulated by PARMELA, compared with the analytical result

62 Correlated project emittance when Δσ nr = 0, and Correlated slice emittance when Δr n =0,simulated by PARMELA, compared with the analytical result

63 Evolution of the two kinds of emittance in a beamline with solenoid, drift tube and accelerating linac section Magnetic length of solenoid (m) 0.22 Length of the drift tube (m) 0.78 Peak magnetic field on axis (Gauss) 2200 Gradient of linac section(mv/m) 17.0 Length of the linac section (m) 6.0

64 Correlated project emittance when Δσ nr =0, and Correlated slice emittance when Δr n =0,simulated by PARMELA, compared with the analytical result

65 Correlated project emittance when Δσ nr = 0, and Correlated slice emittance when Δr n =0,simulated by PARMELA, compared with the analytical result

66 3.4 The Emittance Inside a Slice & Wave Breaking Wave Breaking: 1) r(z) independent of r(0) ( ) 0 0 dr z dr = 2) Transverse momentum p r (r) with multi-solution Z Wave Breaking

67 Correlated slice emittance when Δr n =0,simulated by PARMELA for initial emittance of 4.2mm.mrad and 12mm.mrad, compared with the analytical result

68 Wave breaking The phase space evolution for initial emittance of 4.2mm.mrad (lower) and 12mm.mrad (upper)

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71 Thanks!