Accelerator Physics Particle Acceleration. G. A. Krafft Old Dominion University Jefferson Lab Lecture 7

Transcription

1 Accelerator Physics Particle Acceleration G. A. Krafft Old Dominion University Jefferson Lab Lecture 7 Graduate Accelerator Physics Fall 5

2 v z Convert Fundamental Solutions Convert usual phase space variables z cos z cos I I I I I I I I I tan I I I I I Points of hyper-ellipsoid z cos z cos cos z cos z cos z cos cos z cos I I I II II II I I I II II II I cos II sin y y z I y I I y z II y II II y y I y I I y II y II II Graduate Accelerator Physics Fall 5

3 Set all derivatives zero I, II z, y I, II d, y sin d Projected Ellipse Beam size, II y, d y d I, II z sin, y I, II II y, E y, I I E, y II, y y, y, E y, I, y II, y A I A, y II, y, y I, y II, y A, y E E, y, y E, y I, y, y, y, y, y E A, y, y, y, y I I E II II II II Graduate Accelerator Physics Fall 5

4 Beam Tilt Project -y plane E E, y I, y II, y y I cos cos I y I I II II y II II E I, II y I, II I, II I II EE I cos cos I y I I y II II y II II tan E E y I I II II Graduate Accelerator Physics Fall 5

5 Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 7 Coupled Betatron Motion I 5 USPAS, Fort Collins, CO, June -, 3 Beam sizes a b a y y ~ ~ y y y y a a Ellipse equation ~ ~ y y a y a a y a Ellipse rotation parameter y y y y y a a y y y cos cos ~ ~ ~

6 Aisymmetric Rotational Distribution Electrostatic accelerator Gaussian distribution Fermilab electron cooling Solenoid Rotational distribution The electron beam distribution is aially symmetric, and uncoupled at the cathode: Ξ B T where T rc mktc / P is the thermal emittance of the beam Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II 6 USPAS, Fort Collins, CO, June -, 3

7 Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II 7 USPAS, Fort Collins, CO, June -, 3 Aisymmetric Rotational Distribution At the eit of the solenoid the electron beam distribution is still aially symmetric T B T in Φ Ξ Φ Ξ where Φ c P eb / is the rotational focusing strength of the solenoid edge B is the solenoid magnetic field.

8 Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II 8 USPAS, Fort Collins, CO, June -, 3 The eigen-vectors of the rotational distribution: ˆ i i i i v, ˆ i i i i v It corresponds to u = /, / Then, the matri Vˆ is ˆV Aisymmetric Rotational Distribution

9 Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II 9 USPAS, Fort Collins, CO, June -, 3 4D-emmitance conservation: T Rotational emittance estimate T rot r r r r Comparing left and right hand sides of the equation T T in U V UV Ξ ˆ / / / / ˆ ˆ One obtains.,,, T T T T Aisymmetric Rotational Distribution

10 Spin Rotators for Figure-8 Collider Ring [cm] Figure-8 Collider Ring - Footprint z [cm] total ring circumference ~ m 6 deg. crossing Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II USPAS, Fort Collins, CO, June -, 3

11 -.5 BETA_X&Y[m] DISP_X&Y[m] 5.5 Spin Rotator Ingredients 3 BETA_X BETA_Y DISP_X DISP_Y 3 Arc end BL =.9 Tesla m 8.8 BL = 8.7 Tesla m 4.4 Spin rotator ~ 46 m Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II USPAS, Fort Collins, CO, June -, 3

12 BETA_X&Y[m] 5 5 Locally Decoupled Solenoid Pair BL = 8.7 Tesla m BETA_X BETA_Y BETA_Y BETA_X 7.93 solenoid 4.6 m decoupling quad insert solenoid 4.6 m M = C C Hisham Sayed, PhD Thesis ODU, Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II USPAS, Fort Collins, CO, June -, 3

13 - BETA_X&Y[m] DISP_X&Y[m] 5 Locally Decoupled Solenoid Pair BL = 8.7 Tesla m BETA_X BETA_Y DISP_X DISP_Y 7.93 solenoid 4.6 m decoupling quad insert solenoid 4.6 m M = C C Hisham Sayed, PhD Thesis ODU, Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II USPAS, Fort Collins, CO, June -, 3 3

14 3 BETA_X&Y[m] B E T A _ X & Y 3 [ m ] M o n S e p 6 7 : 4 4 : 4 5 O p t i M - M A I N : - C : \ W o r k i n g \ E L I C \ M E I C \ O p t i c s \ 5 G e V E l e c t e. R i n g \ h a l f _ r i n g _ i n _ s t r a i g h t _ 8 B 8 E T BA E_ TX DA I _ SY DP I _ SX P _ Y D I S P _ X & Y [ m ] DISP_X&Y[m] - Universal Spin Rotator - Optics 5 GeV 88 BETA_X BETA_Y DISP_X DISP_Y 374 BL =.9 Tesla m 8.8 BL = 8.7 Tesla m 4.4 Spin rotator ~ 46 m Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II USPAS, Fort Collins, CO, June -, 3 4

15 Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II 5 USPAS, Fort Collins, CO, June -, 3 Ionization Cooling in an Aially Symmetric Channel A single-particle phase-space trajectory along the beam orbit can be epressed as:, ) ( ˆ ) ( ˆ Re ) ˆ( )) ( ( )) ( ( s i s i e s e s s v v One can rewrite the above equations in the following compact form ) ( ) ( ˆ ) ( ˆ s s s a V where ) ( ˆ ), ( ˆ ), ( ˆ ), ( ˆ ) ( ˆ s s s s s v v v v V )) ( sin( )) ( cos( )) ( sin( )) ( cos( ) ( s s s s s a

16 Verte-to-plane Transformer Insert Solenoid Skew-quadrupole system Uncoupled aial-symmetric distribution Rotational distribution P Flat distribution Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II 6 USPAS, Fort Collins, CO, June -, 3

17 Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II 7 USPAS, Fort Collins, CO, June -, 3 Verte-to-plane Transformer Insert Eigen-vectors of the decoupled motion in the coordinate system rotated by deg. F F i i i i i rotation Rotational eigen-vectors F F i F if

18 Verte-to-plane Transformer Insert Focusing system with 45 difference between the horizontal and vertical betatron phase advances will transform the initial verte distribution into the flat one The resulting D emittances are as follows T T,. Lattice implementation Twiss functions, beam sizes etc. Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II 8 USPAS, Fort Collins, CO, June -, 3

19 BETA_X&Y[m] Betatron size X&Y[cm] Verte-to-plane Transformer Insert AlphaXY[-, +] - 5 BETA_X&Y[m].5 PHASE/(*PI).5 5 BETA_X BETA_Y BETA_Y BETA_X.6647 BETA_X BETA_Y BETA_Y BETA_X.6647 A Ay AlphaXY.6647 Q_ Q_ Teta Teta.6647 E kin = MeV, T c =. ev, R c =.5 cm, B sol = kg, = cm, = cm Operated by JSA for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 9 Coupled Betatron Motion II 9 USPAS, Fort Collins, CO, June -, 3

20 Northern Illinois Center for Accelerator and Detector Development Generation and Dynamics of Magnetized Beams for High-Energy Electron Cooling * Philippe Piot, Department of Physics and Northern Illinois Center for Accelerator & Detector Development, Northern Illinois University, DeKalb IL 65 Accelerator Physics Center, Fermi National Accelerator Laboratory, Batavia IL 65 Yin-e Sun, Advanced Photon Source, Argonne National Laboratory, Argonne IL 6439 International Workshop on Accelerator Science & Technologies for future electron-ion colliders (EIC 4), Jefferson Lab, March 7-, 4 *sponsored by the DOE awards DE-FG-8ER453 to Northern Illinois University and DE-AC-7CH359 to the Fermi Research Alliance LLC.

21 Outline Introduction Features and parameterization of magnetized beams Formation of magnetized bunches: methods and limitations, eperiments in rf gun. Transport and Manipulation: transverse matching, longitudinal manipulations, decoupling into flat beams. Outlook P. Piot, EIC 4, JLab, Mar. 7-, 4

22 Required Electron-Beam Parameters Cooling interaction time (magnetized) (not magnetized) (magnetized) magnetized cooling less dependent on e- beam transverse emittance (to what etent?) (not magnetized) electron-cooling accelerator provides beam eventually matched to coolingsolenoid section P. Piot, EIC 4, JLab, Mar. 7-, 4

23 e.g. see S. Nagaitsev, et al, PRL96, 448 (6) e.g. see I. Ben-Zvi, et al., Proc. PAC, p. 48 () Cooler configurations low-energy coolers: lattice (bends) embedded in magnetic fields, based on DC electron sources, no further acceleration or bunching, needed. 3 kev, 3 A cooler produced by Budker INP for IMP, Lanzhou (China) high-energy coolers: medium energies required (5- MeV), acceleration in SCRF linac bunching lumped solenoidal fields matching early concept for RHIC e-cooling P. Piot, EIC 4, JLab, Mar. 7-, 4 3

24 High-energy coolers magnetizedbeam injector matching mode/converter bunching acceleration debuncher injector: produces bunched beam for RF acceleration debuncher: matched electron bunch length to ion-beam s, matching + mode/converter sections: repartition physical emittances, match in cooling-solenoid section. matching cooling section dump or energy recovery P. Piot, EIC 4, JLab, Mar. 7-, 4 4

25 adapted from Y.-E Sun, Dissertation U. Chicago (5) Beam dynamics regimes (round beams) Radial envelope (s ) equation in a drift (Lawson): space charge emittance pressure : generalized perveance : uncorrelated geometric emittance : magnetization P. Piot, EIC 4, JLab, Mar. 7-, 4 angular momentum contribution 5

26 Features & Parameterization possible parameterization of coupled motion between degrees of freedom has been etensively discussed; see: D.A. Edwards and L.C. Teng, IEEE Trans. Nucl. Sci., 3, pp (973). I. Borchardt, E. Karantzoulis, H. Mais, G. Ripken, DESY 87-6 (987). V. Lebedev, S. A. Bogacz, ArXiV:7.556 (7). A. Burov, S. Nagaitsev, A. Shemyakin, Ya. Derbenev, PRSTAB 3, 94 (). A. Burov, S. Nagaitsev, Ya. Derbenev, PRE 66, 653 (). Simpler description that provides the necessary insights.. P. Piot, EIC 4, JLab, Mar. 7-, 4 6

27 A simple description of coupled motion Consider the 44 beam matri Introduce the correlation matri: Beam matri takes the form: where The correlation subjects to as transforms C provides information on the coupling only. P. Piot, EIC 4, JLab, Mar. 7-, 4 7

28 K.-J. Kim, PRSTAB 6, 4 (3) D. A. Edwards, unpublished () Beam matri for a round magnetized beam At a waist, the matri of a magnetized (round) beam is where and the magnetization is The eigen-emittances of this beam matri are: where the eigen-emittances can be mapped into physical emittances using a skewed beamline decoupling when P. Piot, EIC 4, JLab, Mar. 7-, 4 8

29 Formation of magnetized bunches Cathode immersed in an aial B field Sheet beams at birth (with subsequent flat-to-round beam converter) shaped cathode, line-laser focus Nonlinear optics (speculative) mode converter Y. Derbenev, University of Michigan report UM-HE-98-4 (998) G. Florentini, et al., Proc. PAC95, p. 973 (996) P. Piot, EIC 4, JLab, Mar. 7-, 4 9

30 Cathode in a magnetic field electrons born in an aial B field CAM upon eit of solenoid field ( becomes purely kinetic. ): CAM P. Piot, EIC 4, JLab, Mar. 7-, 4 3

31 Emittance vs magnetization effective emittance magnetization The emittance has a lower-bound value : where is the ecess in kinetic energy during emission Practically, contributions. includes other P. Piot, EIC 4, JLab, Mar. 7-, 4 3

32 P. Piot et al. IPAC3; C-X. Wang, FEL6, 7 (6) X. Chang, I. Ben-Zvi, J. Kewisch AAC4 (4) Eample of 3.-nC magnetized bunch high-charge bunch subject to emittance degradation proper optimization (emittance compensation) 4-D emittance comparable to round beams. eigenemittances evolution in ASTA photoinjector P. Piot, EIC 4, JLab, Mar. 7-, 4 3

33 Y.-E Sun et al, PRSTAB 7, 35 (4) Measuring (kinetic) angular momentum Kinetic angular momentum can be measured using a slit technique (similar to emittance) beam at slits beam at observation point The beam s average angular momentum is given by P. Piot, EIC 4, JLab, Mar. 7-, 4 : rms beam size at slit () and observation screen (), : aial momentum : drift length between locations () and (). 33

34 Y.-E Sun et al, PRSTAB 7, 35 (4) Eperimental generation in a photoinjector Fermilab A normal-conducting photoinjector (decommissioned), 5 MeV, charge up to nc,~3- ps bunch main focus was conversion to flat beams P. Piot, EIC 4, JLab, Mar. 7-, 4 34

35 rotation angle (deg) Y.-E Sun et al, PRSTAB 7, 35 (4) Eperimental generation in a photoinjector linear scaling with B field on photocathode magnetic field B on cathode (G) P. Piot, EIC 4, JLab, Mar. 7-, 4 35

36 Y.-E Sun et al, PRSTAB 7, 35 (4) Eperimental generation in a photoinjector weak dependence, quadratic scaling with laser spot size on photocathode. measured kinetic angular momentum CAM from applied B field P. Piot, EIC 4, JLab, Mar. 7-, 4 36

37 R. Brinkmann et al., PRSTAB 4, 535 () Y. Derbenev, University of Michigan report UM-HE-98-4 (998) Decoupling into flat ( / y ) beam Transport of magnetized bunches while preserving is challenging, Use of round-to-flat beam transformer to convert into uncoupled (flat) beam eigen-emittances maps into physical transverse emittances: P. Piot, EIC 4, JLab, Mar. 7-, 4 37

38 P. Piot, et al, PRSTAB 9, 3 (6) Decoupling into flat beam: eperiments () Same eperimental setup as used for generation of CAM-dominated beams simulations.5 nc eperiments simulations P. Piot, EIC 4, JLab, Mar. 7-, 4 38

39 Decoupling into flat beam: eperiments () normal emittances map into the flatbeam emittance large eperimental uncertainties for smallest emittance meas. P. Piot, EIC 4, JLab, Mar. 7-, 4 39

40 Outlook + open questions magnetized beam from a SCRF gun: flu concentrator around cathode? flat beam at cathode [J. Rosenzweig, PAC93 showed (, )=(95,4.5) m] needed and? and limit on 4-D emittance? planned future eperiment at ASTA P. Piot, EIC 4, JLab, Mar. 7-, 4 4