An Introduction to Plasma Accelerators

Transcription

1 An Introduction to Plasma Accelerators Humboldt University Research Seminar > Role of accelerators > Working of plasma accelerators > Self-modulation > PITZ Self-modulation experiment > Application Gaurav Pathak Universität Hamburg / PITZ,DESY May 16, 2014

2 Role of High Energy Particle Accelerators Man has always been wondering about the world around him What is world made up of? What holds it together? Built various devices to find answers Wavelength of the probe should be smaller than the size of the object tobeprobed De Broglie Wavelength 2 To probe matter on smaller scale requires particles with higher energy Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 2

3 Particle Accelerator Development 1919 Rutherford gets the first nuclear reactions using natural alpha rays (radio activity) of some MeV).«He realize already that he will need many MeV to study the atomic nucleus Ising proposes the acceleration using a variable electric field between drift tubes(the father of the LINAC) Wideroe uses Ising principle with an RF generator, 1MHz, 25 kv and accelerate potassium ions up to 50 kev. 1928Cockcroft & Walton start designing an 800 kv generator encouraged by Rutherford. 1932Generator reaches 700 kv and Cockcroft & Walton split lithium atom with only 400 kevprotons. «received the Nobel Prize in Veksler proposed the concept of using electron beam driven plasma waves to accelerate charge Particles T. Mainman invented the laser Tajima and Dawson proposed to use laser beam to excite plasma wave for electron acceleration. The Mechanism called LWFA (Laser wakefield acceleration) Chen et. al. proposed the basic mechanism of the PWFA (Plasma wakefield acceleration) in the linear regime using electron beam A. Caldwell et. al proposed to use proton driven PWFA to accelerate the particles. A breif history and review of accelerators P.J.Brayant, CERN, Geneva E. Esarey, P. Sprangle, Overview of plasma-based accelerator concepts, IEEE transaction on plasma science, Vol. 24, No. 2, April 1996 Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 3 80 kev Cyclotron at LBNL (1930 ) 7 TeV Synchrotron at CERN

4 Conventional and Wake-field Accelerators Conventional accelerator based on RF cavities Large Hadron Collider at CERN Limited acceleration gradient : E ~50 MV/m (due to material break down) Several kilometer size accelerator for TeV energy Require huge money and human resources A voltage generator induces an electric field inside the RF cavity. Its voltage oscillates with radio frequency (~1.3GHz). e - The electron always feel the force in the forward direction. E ~ 50 MV/m 27 km circumference $6 billion+? An electron source injects particles into the cavity in phase with the variable voltage. Injection at the correct phase ensures that electron will never face the deaccelerating field. Wake-field acceleration based on plasma waves Plasma supports high electric field : E ~ 100 GV/m (no breakdown limit) Compact size accelerator of few meters size Much lower cost Wake-field acceleration Small laboratories can also afford it!!! E ~ GV/m (density dependent) Quasi-monoenergetic laser-plasma acceleration of electrons to 2 GeV, X. Wang et. al., Nature Communications 4, Article number: 1988 doi: /ncomms2988 Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 4

5 Wakefield Acceleration Ponderomotive Force r r r r r r F = e [(r. )E + (v / c) B] ~ I p 1 r = 0 1 L 1 Electrons will be pushed from high to low intensity region of laser pulse. Laser pulse E z ~ n e (cm -3 ) F P F P Plasma Wave Laser Wake-Field Acceleration cτ laser λ p / 2 Space charge Force Electrons will be pushed by space charge force of charged particle beam. Plasma Wake-Field Acceleration Electron bunch F s F s LWFA - E z ~ 100 GV/m for n e = cm -3 PWFA - E z ~ 3 GV/m for n e = cm -3 2σ E. Esarey, P. Sprangle, Overview of plasma-based accelerator concepts, IEEE transaction on plasma science, Vol. 24, No. 2, April 1996 Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 5

6 1-D Theory for PWFA. 0 - Equation of continuity.!" -Equation of motion Let # $%&'& ()'*+, -)& ()'*+,. $)/+0/-&+*1 (0) +1 -)& $/1$&2&+*1 &(. # Keeping only linear terms and combining both equation yields the equation of density perturbation Consider a 1-D case for beam 9 :6 + 62" where 0*;1/ '0/;&<) 0-)/ ()'*+, 9=*/&< ()%+& ;0<+*1 Substituting (2) in (1) and solving yields the density perturbation induced by the injected beam A BCDEF A B G6H B I A B G6H B IJK K A B G6H B ILK Substituting this into Maxwell s first equation where " 5 4 #) E R Q >?.4). " gives 4) <1'N, N :65 +J0 M2) N : N :65 +L0 Which shows that E field is 90 P out of phase with density perturbation E. Esarey, P. Sprangle, Overview of plasma-based accelerator concepts, IEEE transaction on plasma science, Vol. 24, No. 2, April 1996 Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 6

7 LWFA vs PWFA Dephasing: The length in the laboratory frame in which the accelerating electrons slips by 90 o in phase with respect to the plasma wave. For gaining 1GeV energy dephasing length would be L dph ~ 1 mm - for n e ~ cm -3 L dph ~ 1 cm - for n e ~ cm -3 L dph ~ 10cm - for n e ~ cm -3 L dph ~ 1m - for n e ~ cm -3 λ p /2 LWFA - E z ~ 100 GV/m for n e = cm -3 PWFA - E z ~ 3 GV/m for n e = cm -3 L dph = λ p3 /λ 2 L dph = λ p3 /λ 2 Although in PWFA the gradient is not as high as already achieved in LWFA, the 1-GeV/m gradient is much larger than that achieved in any accelerating metallic structure. E. Esarey, C. B. Schroeder, and W. P. Leemans, Physics of laser-driven plasma-based electron accelerators Reviews of Modern physics, vol. 81, Jul-Sep Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 7

8 Some references There were many other great contributions and milestones from many people. Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 8

9 Motivation A Proton driven plasma wakefield acceleration was proposed by A.Caldwellet.al.in2009 A proton driver suck the plasma electrons leading to the electron density enhancement on-axis This sets the plasma electrons into oscillation. The oscillation of plasma electron set up an oscillating electric field given by 240ST R. " Why short proton bunches required? # σ To maximize the plasma wavelength should have a definite relation to the length of the driving bunch: 2σ 1 10.V < RW The CERN SPS bunch has length ~12cm(120mm). How to generate short proton bunches? 3.16 ;1/10.Z < RW, M1 ;1/ 10.V < RW 0.31 ;1/10.[ < RW Tradeoff between,σ &( A. Caldwell et. al. Proton-driven plasma-wakefield acceleration, Nature Physics 5, (2009) Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 9

10 Self-modulation To generate a short proton bunches a technique viz. self modulation is proposed by N. Kumar and A. Pukhov in After passing through knife Before passing through knife Simply speaking if a charged particle bunch travelling through plasma is long in comparison to the plasma wavelength then it can get self-modulated, splitting itself into short bunches via electric fields of plasma. Electron beam before passing through plasma Plasma E field N. Kumar and A. Pukhov, Self-modulation instability of a long proton bunch in plasmas, PRL104, (2010) Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 10 Electron beam after passing through plasma This principle can be applied to the long electron bunch also.

11 Self-Modulation Experiments at PITZ > Favorable circumstances P 10.V < RW 1 Very high level photo injector test facility Worldwide unique laser system (pulse shaper) Well developed diagnostics (high resolution electron spectrometer, etc.); soon: transverse deflecting cavity + dispersive section for longitudinal phase space measurements > Needed for preparation: PIC simulations OSIRIS (full PIC code) HiPACE (quasi-static) - Efficiency Osiris Simulations M.Gross et. al, Preparations for a plasma wakefield acceleration (PWA) experiment at PITZ, NEMA, 740 (2014) Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 11

12 HiPACE - Algorithm of the Code At each time step Particle positions: Calculating particle position \,0 Interpolation: Evaluate force on the particles,! ` Deposition: Calculating current on the grid \,0 ^ ($ (+ a < ` 0 \! Integration of the field equation: Updating field,! ^ 4 <! 64^ 4+ 4! 4+ 6< Quasi-static or frozen field approximation converts Maxwell s equations into electrostatic equations Maxwell equations in Lorentz gauge Transforming to co-moving frame Quasi-static approximation Reduced Maxwell equations 4 < : b c 4 < ^ 4 < : d4e f:6<+ +g g 6< 4 4f 4 4: 4 4f 4 <4g 4 4f 6 bc 4 < ^ 6 d4e Solving these reduced equation saves the time. Quasi-static codes are already tested and shows good resembles with full PIC codes.* Courtesy C. Benedetti, T. Mehrling, A. M. de la Ossa, J. Osterhoff C. Schroeder, DESY *C.Huang et.al. doi: / /46/1/026 Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 12

13 HiPACE code Input and Output 1. Beam defined in HiPACE code Beam density rms beam size in x,y direction Beam length in z direction Mean energy rms relative energy spread Normalized emittance in x,y direction Beam from ASTRA 2. MATLAB formatted ASTRA beam suitable for HiPACE input Choose 1 st or 2 nd HiPACE Outputs Beam density, " Plasma density, " Longitudinal electric field, "! h Beam energy modulation Courtesy C. Benedetti, T. Mehrling, A. M. de la Ossa, J. Osterhoff C. Schroeder, DESY Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 13

14 Initial Beam Parameters Two simulation were performed to see the effect of different beam size. Beam parameters Setup (1) Setup (2) Total charge, pc X rms beam size, µm Y rms beam size, µm (1) Z rms, mm Average Momentum, MeV/c Momentum Spread, kev/c i j, mm mrad i k, mm mrad Number of particles 200, ,000 Plasma Density P 10.V < RW (2) Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 14

15 Results - Energy Modulation and Ez Setup 1 Setup 2 Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 15

16 Parameters of Setup (2) ASTRA Input Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 16

17 Phase space after plasma Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 17

18 PITZ Self-modulation experiment approach Ionization with ArF laser (top view) Plasma Cell Design An ionization laser pulse energy of a few100l is needed to generate a plasma channel of 10mm diameter and 60 mm length with a plasma density of10.v < RW. M.Gross et. al, Preparations for a plasma wakefield acceleration (PWA) experiment at PITZ, NEMA, 740 (2014) Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 18

19 Application - Intense X-rays from Undulator h-harmonic number Undulator radiation Wavelength of radiation : Tunability: by varying electron energy, period and amplitude of magnetic field Undulator radiation Accelerator Undulator e-beam dump Synchrotron radiation Relativistic electrons in a magnetic field follow a curved trajectory and therefore they are accelerated. The acceleration results in emission of radiation into a narrow cone (lab frame of reference). The Science and Technology of Undulators and Wigglers J.A. Clarke, Oxford Univ. Press Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 19

20 Application - Intense X-rays from Undulator Energy of the electrons is higher (synchrotrons are operating with GeV electrons) Wavelength of the undulator field is larger (of the order of cm in the laboratory frame) SLAC Bending magnet 3 km ~50GeV Synchrotron radiation 50GeV in 5m for n e ~ cm -3 Key element V.Malka et. al., Principle and applications of compact laser plasma accelerators, Nature Physics 4, (2008) Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 20

21 Summary Features of plasma accelerated electron beams High peak current (up to 100 ka) Ultrashort bunch length (down to 10fs) Compact & low cost Excellent emittance High bunch charge (up to nc) Energy Spread Reproducibility of beam The field is full of excitement! E. Esarey, C. B. Schroeder, and W. P. Leemans, Physics of laser-driven plasma-based electron accelerators Reviews of Modern physics, vol. 81, Jul-Sep Gaurav Pathak An Introduction to Plasma Accelerators May 16, 2014 Page 21