l20 advanced manip - northern illinois...

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

PHYS 790-‐D Special topics in Beam Physics, Fall 2014 1

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)


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

•  The electrosta+c field (in the ref. frame) give rise to an electromagne+c field in the laboratory frame


EEE = �(EEE0)� �2

� + 1��(��.EEE0)

BBB = ��(�� ⇥EEE0)

r2�(rrr0) =⇢(rrr0)

"0

Space-‐charge effects

•  The force can be computed from

•  in order to avoid any emiXance growth we want the force to be a linear func+on of the spa+al coordinate (see HW1)

•  which means


FFF = q(EEE + v�� ⇥BBB)

F

F

F / x

x

x

x

x

x ⌘ (x, y, z)

E

E

E

0 / x

x

x

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 and depends on the aspect ra+o


Verifica/on via numerical simula/ons

•  as


Prac/cal realiza/on •  Two methods: – 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


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)


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


Linear-‐ramp genera/on

•  Downstream of bunch compressor •  So finally !the parameters provide control over the correla+on within the LPS


beam energy

Final distribu/on •  Assume ini+al Gaussian distribu+on,

•  charge conserva+on yields with and (accounts for uncorrelated δ).


Examples of possible distribu/ons

•  generated shapes:


HEAD HEAD

Experimental realiza/on

•  FLASH facility


Head

Standard compression

Ramped bunch 200 A Ramped bunch 1 kA

Ramped bunch 0.5 kA

Head Head

Head

(700 MeV, 0.5 nC)

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


Microbunched beam forma/on via IFEL

•  The beam has a dura+on •  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


T � �/c

Experimental realiza/on

•  re


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


bunching at higher harmonic via the “echo” effect

•  as


hXps://portal.slac.stanford.edu/sites/ard_public/>d/facili+es/nlcta/Pages/Echo-‐enabled-‐Harmonic-‐Genera+on.aspx

Brief theory

•  ini+al distribu+on (assume coa+ng beam)

•  a]er modulator 1 ( )

•  final distribu+on


mod 1 chic 1 mod 2 chic 2

mod 1 chic 1

mod 2 chic 2

beam “func/on generator”

•  can expand the previous technique to actually produce longitudinal phase spaces that follow analy+cal func+on

•  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


phase delay

phase delay

examples of synthe/zed phase spaces

•  The laser para-‐ meters are selected to construct the series (3 terms)


1 laser 2 lasers 3 lasers

l20 advanced manip - northern illinois...

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