Advanced beam manipula/ons

Transcription

1 Advanced beam manipula/ons beam manipula+ons are two fold: transverse (focusing, shaping, ) longitudinal (tailoring the current of energy spectrum of a beam) Transverse shaping is rather straigh>orward (it involves using nonlinear op+cal elements beyond the simple element introduce in this class) Longitudinal shaping is complex and an intense research topics 1

2 Mo/va/ons Why does one need to shape a beam minimizing collec+ve effects, taking advantage of collec+ve effects (wakefield for beam- driven accelera+on) produce very short bunches slicing, microbunches (train of bunch) Shaping can also be performed using transforma+ons that couple two degrees of freedom (we will not study these here) 2

3 Space- charge effects Space charge can be treated as an electrosta+c problem in the bunch s reference frame We have to solve Laplace s equa+on r 2 (r 0 )= (r0 ) The electrosta+c field (in the ref. frame) give rise to an electromagne+c field in the laboratory 2 frame E = (E 0 ) B = ( E 0 ) " 0 +1 (.E0 ) 3

4 Space- charge effects The force can be computed from F = q(e + v B) in order to avoid any emixance growth we want the force to be a linear func+on of the spa+al coordinate (see HW1) F / x x (x, y, z) which means E 0 / x 4

5 Mi/ga/on of space- charge effects what is the distribu+on that leads to such a force? a uniformly charge 3D ellipsoidal distribu+on the fields are where the form factors obey depends on the aspect ra+o and 5

6 Verifica/on via numerical simula/ons as 6

7 Two methods: Prac/cal realiza/on self shaping (space charge expansion for the beam to expand into a 3D ellipsoidal bunch) this is the reverse process of the collapse of unform oblate spheroid to a disk shaping of a photo- emission laser 7

8 Linear- ramp genera/on distribu+on o]en use in some accelera+on schemes can be accomplished using a nonlinear longitudinal phase- space transforma+on Exploit nonlinear effects in bunch compression with two accelera+ng cavi+es opera+ng at two different frequencies (an extension of HW3 problem on nonlinear bunch compression) 8

9 Linear- ramp genera/on: theory 1D- 1V model of the LPS dynamics Coordinates of electron downstream of source: Downstream of a 2- f linac with voltage 9

10 Linear- ramp genera/on Downstream of bunch compressor So finally beam energy!the parameters provide control over the correla+on within the LPS 10

11 Final distribu/on Assume ini+al Gaussian distribu+on, charge conserva+on yields with and (accounts for uncorrelated δ). 11

12 Examples of possible distribu/ons generated shapes: HEAD HEAD 12

13 Experimental realiza/on FLASH facility Standard compression Ramped bunch 0.5 ka Head Head Ramped bunch 200 A Ramped bunch 1 ka Head Head (700 MeV, 0.5 nc) 13

14 Microbunched beams Beams consis+ng of a train of ultra- short pulse have also important applica+on (mostly in coherent- radia+on source, and as injector for short- wavelength op+cal accelerators) An obvious scheme is the FEL or inverse FEL process In order not to rely on the radia+on produced by an FEL one can seed the undulator with a laser 14

15 Microbunched beam forma/on via IFEL The beam has a dura+on T /c the laser and beam couples within an undulator so that net energy exchange occurs The energy modula+on is converted into a density modula+on within the undulator if undulator is long enough with a chicane- based bunch compressor 15

16 re Experimental realiza/on 16

17 arosecond structures The scheme is limited by the laser wavelength and the bunch energy spread How can one produce shorter bunches use a cascaded scheme 17

18 bunching at higher harmonic via the as echo effect hxps://portal.slac.stanford.edu/sites/ ard_public/>d/facili+es/nlcta/pages/echo- enabled- Harmonic- Genera+on.aspx 18

19 Brief theory ini+al distribu+on (assume coa+ng beam) a]er modulator 1 ( ) mod 1 chic 1 mod 2 chic 2 mod 1 chic 1 final distribu+on mod 2 chic 2 19

20 beam func/on generator can expand the previous technique to actually produce longitudinal phase spaces that follow analy+cal func+on phase delay phase delay very similar to echo scheme but laser frerquency, field amplitude and rela+ve phases are chosen to synthe+ze arbitrary waveform in the longitudinal phase space 20

21 examples of synthe/zed phase spaces The laser para- meters are selected to construct the series (3 terms) 1 laser 2 lasers 3 lasers 21