EuCARD-2 Enhanced European Coordination for Accelerator Research - - PDF document

CERN-ACC-SLIDES-2014-0114

EuCARD-2

Enhanced European Coordination for Accelerator Research & Development

Presentation Beam Propagation, effects and parameters of the accelerated beam

Assmann, R (DESY)

27 November 2014

The EuCARD-2 Enhanced European Coordination for Accelerator Research & Development project is co-funded by the partners and the European Commission under Capacities 7th Framework Programme, Grant Agreement 312453. This work is part of EuCARD-2 Work Package 7: Novel Accelerators (EuroNNAc2).

The electronic version of this EuCARD-2 Publication is available via the EuCARD-2 web site <http://eucard2.web.cern.ch/> or on the CERN Document Server at the following URL: <http://cds.cern.ch/search?p=CERN-ACC-SLIDES-2014-0114>

CERN-ACC-SLIDES-2014-0114

R.W. Aßmann

Leading Scientist DESY

CERN, 27.11.2014

Beam Propagation

effects and parameters of the accelerated beam

Ralph Aßmann | CAS | 27.11.2014 | Page 2

Content

• 1. Accelerators – From Conventional Techniques to

Plasmas

• 2. The Linear Regime
• 3. The Non-Linear Regime
• 4. Tolerances

Ralph Aßmann | CAS | 27.11.2014 | Page 3

Acceleration: Conventional and Advanced

Surfer gain velocity and energy by riding the water wave! Charged particles gain energy by riding the electromagnetic wave!

generate light pulses with very large transverse fields: couple fields to our particles!

Ralph Aßmann | CAS | 27.11.2014 | Page 4

Governed by Maxwells Equations

∇ · E = ρ ǫ0 ∇ × E = −∂B ∂t ∇ · B = 0 ∇ × B = µ0J + ǫ0µ0 ∂E ∂t

E = Electrical field intensity B = Magnetic flux density J = Total current density ρ = Total charge density µ0 = Permeability of free space ǫ0 = Permittivity of free space

Very few acceleration issues require quantum mechanics (e.g. spin polarization).

Ralph Aßmann | CAS | 27.11.2014 | Page 5

Lorentz Force F

F = q (E + v × B)

q = Charge v = Velocity

Longitudinal electrical field to accelerate a particle Transverse magnetic field to guide a particle

Ralph Aßmann | CAS | 27.11.2014 | Page 6

RF Acceleration in Metallic Structures

>

• >
• >
• Courtesy Padamse, Tigner

Courtesy N. Walker

From Ising’s and Wideröe’s start to 21st century RF technology.

“Runzelröhre”

Ralph Aßmann | CAS | 27.11.2014 | Page 7

High Gradient – High Frequency – Small Dimensions

Band Designator Frequency [GHz] Gradient [MV/m] Cell length [cm] Comments L band 1 to 2 24 15 – 7.5 This band is used by super-conducting RF technology. The dimensions are large, accelerating gradients are lower and disturbing wakefields are weak. S band 2 to 4 21 7.5 – 3.8 Technology of the SLAC linac that was completed in 1966. This is still the technology behind many accelerators.

Ralph Aßmann | CAS | 27.11.2014 | Page 8

High Gradient – High Frequency – Small Dimensions

S band 2 to 4 21 7.5 – 3.8 Technology of the SLAC linac that was completed in 1966. This is still the technology behind many accelerators. C band 4 to 8 35 3.8 – 1.9 Newer technology developed in Japan and used for the construction

• f the SACLA linac in

Japan. Band Designator Frequency [GHz] Gradient [MV/m] Cell length [cm] Comments

Ralph Aßmann | CAS | 27.11.2014 | Page 9

High Gradient – High Frequency – Small Dimensions

C band 4 to 8 35 3.8 – 1.9 Newer technology developed in Japan and used for the construction

• f the SACLA linac in

Japan. X band 8 to 12 70 – 100 1.9 – 1.3 Technology developed from the 1990’s onwards for linear collider designs, like NLC and CLIC. The cell length is up to a factor 10 shorter than in L band. Band Designator Frequency [GHz] Gradient [MV/m] Cell length [cm] Comments

Ralph Aßmann | CAS | 27.11.2014 | Page 10

High Gradient – High Frequency – Small Dimensions

X band 8 to 12 70 – 100 1.9 – 1.3 Technology developed from the 1990’s onwards for linear collider designs, like NLC and CLIC. The cell length is up to a factor 10 shorter than in L band. Ku band 12 to 18 n/a 1.3 – 0.8 K band 18 to 27 n/a 0.8 – 0.6 Ka band 27 to 40 70 0.6 – 0.4 Investigated for a possible CLIC linear collider technology at 30 GHz but abandoned after damage problems. V band 40 to 75 n/a 0.4 – 0.2 W band 75 to 110 > 1000 0.2 – 0.1 Advanced acceleration Band Designator Frequency [GHz] Gradient [MV/m] Cell length [cm] Comments

Ralph Aßmann | CAS | 27.11.2014 | Page 11

High Gradient – High Frequency – Small Dimensions

Band Designator Frequency [GHz] Gradient [MV/m] Cell length [cm] Comments L band 1 to 2 24 15 – 7.5 This band is used by super-conducting RF

• technology. The dimensions are large,

accelerating gradients are lower and disturbing wakefields are weak. S band 2 to 4 21 7.5 – 3.8 Technology of the SLAC linac that was completed in 1966. This is still the technology behind many accelerators. C band 4 to 8 35 3.8 – 1.9 Newer technology developed in Japan and used for the construction of the SACLA linac in Japan. X band 8 to 12 70 – 100 1.9 – 1.3 Technology developed from the 1990’s

• nwards for linear collider designs, like

NLC and CLIC. The cell length is up to a factor 10 shorter than in L band. Ku band 12 to 18 n/a 1.3 – 0.8 K band 18 to 27 n/a 0.8 – 0.6 Ka band 27 to 40 70 0.6 – 0.4 Investigated for a possible CLIC linear collider technology at 30 GHz but abandoned after damage problems. V band 40 to 75 n/a 0.4 – 0.2 W band 75 to 110 > 1000 0.2 – 0.1 Advanced acceleration schemes with ultra high gradients and very short cell lengths.

Plasma acceleration in the > W band

Ralph Aßmann | CAS | 27.11.2014 | Page 12

Transverse to Longitudinal

> Idea: Use a plasma to convert the transverse space charge force of a beam driver (or the electrical field of the laser) into a longitudinal electrical field in the plasma!

• R. Assmann

12

Ralph Aßmann | CAS | 27.11.2014 | Page 13

Reminder: Plasma-Acceleration (Internal Injection)

Works the same way with an . But then usually lower plasma density. Ponderomotive force of laser is then replaced with space charge force of electrons on plasma electrons (repelling).

Ralph Aßmann | CAS | 27.11.2014 | Page 14

Reminder: Plasma-Acceleration (Internal Injection)

Ralph Aßmann | CAS | 27.11.2014 | Page 15

Reminder: Plasma-Acceleration (Internal Injection)

• + -

Ralph Aßmann | CAS | 27.11.2014 | Page 16

Reminder: Plasma-Acceleration (Internal Injection)

Ralph Aßmann | CAS | 27.11.2014 | Page 17

Reminder: Plasma-Acceleration (Internal Injection)

• This proved highly

successful with electron bunches of .

• Small dimensions involved

few !

• Highly compact but also

accelerator: generation, bunching, focusing, acceleration, (wiggling) all in

• ne small volume.
• Energy spread and stability

at the few % level.

Ralph Aßmann | CAS | 27.11.2014 | Page 18

Our Focus: External Injection of Known Beams...

External Injection…

Ralph Aßmann | CAS | 27.11.2014 | Page 19

Foto Laser-Plasmabeschleuniger

SEITE 19

500 mm 0.25 mm

100 mm

Metall (Kupfer) S band Linac Struktur Mikro- Wellen zur Wellener- zeugung

2013

0.05 mm

See lecture M. Kaluza

Ralph Aßmann | CAS | 27.11.2014 | Page 20

Wakefields a la Leonardo da Vinci in 1509…

• R. Assmann

20

Ralph Aßmann | CAS | 27.11.2014 | Page 21

The Linear Regime

> Analytical treatment > Placement of beams in the plasma accelerating structure > Maximum acceleration (transformer ratio) > Optimizations: Energy spread, phase slippage, stability, reproducibility

Ralph Aßmann | CAS | 27.11.2014 | Page 22

Linear Wakefields (R. Ruth / P. Chen 1986)

ε= electrical field z = long. coord. r = radial coord. a = driver radius ωp= plasma frequency kp= plasma wave number t= time variable e= electron charge N= number e- drive bunch

• ω= laser frequency

τ= laser pulse length E0= laser electrical field m= mass of electron Can be analytically solved and treated. Here comparison beam-driven and laser-driven (beat wave).

Ralph Aßmann | CAS | 27.11.2014 | Page 23

Linear Wakefields (R. Ruth / P. Chen 1986)

Accelerating field Transverse field Depends on radial position r Changes between accelerating and decelerating as function of longitudinal position z Depends on radial position r Changes between focusing and defo- cusing as function of longitudinal position z π/2 out of phase

Ralph Aßmann | CAS | 27.11.2014 | Page 24

The Useful Regime of Plasma Accelerators

Two conditions for an accelerator: These two conditions define a useful range of acceleration! Reminder metallic RF accelerator structures: no net transverse fields for beam particles full accelerating range is available for beam usually place the beam on the crest of the accelerating voltage

Ralph Aßmann | CAS | 27.11.2014 | Page 25

Plasma Accelerator

Ralph Aßmann | CAS | 27.11.2014 | Page 26

Plasma Accelerator

Ralph Aßmann | CAS | 27.11.2014 | Page 27

Plasma Accelerator Half of beam is in defocusing regime

Ralph Aßmann | CAS | 27.11.2014 | Page 28

Plasma Accelerator

Ralph Aßmann | CAS | 27.11.2014 | Page 29

Plasma Accelerator Half of beam is in decelerating regime

Ralph Aßmann | CAS | 27.11.2014 | Page 30

Plasma Accelerator

Ralph Aßmann | CAS | 27.11.2014 | Page 31

Plasma Accelerator Beam is in defocusing regime beam explodes

Ralph Aßmann | CAS | 27.11.2014 | Page 32

Plasma Accelerator

Ralph Aßmann | CAS | 27.11.2014 | Page 33

Plasma Accelerator This works, but the bunch sits on the slope of acceleration head gets lower energy than tail energy spread

Ralph Aßmann | CAS | 27.11.2014 | Page 34

Comparison with OSIRIS simulation 50 100 150 200 250 300

• 0.4
• 0.2

0.2 0.4

Longitudinal field Transverse field x10

• 3

cm

17

Plasma density 10

Wz,x / Wz,0

Wz,0 = 30.4 GV/m

z [μm]

Calculation J. Grebenyuk

Ralph Aßmann | CAS | 27.11.2014 | Page 35

Comparison with OSIRIS simulation 50 100 150 200 250 300

• 0.4
• 0.2

0.2 0.4

Longitudinal field Transverse field x10

• 3

cm

17

Plasma density 10

Wz,x / Wz,0

Wz,0 = 30.4 GV/m

z [μm]

Laser pulse Calculation J. Grebenyuk

Ralph Aßmann | CAS | 27.11.2014 | Page 36

Plasma Accelerator This works, but the bunch sits on the slope of acceleration head gets lower energy than tail energy spread

Ralph Aßmann | CAS | 27.11.2014 | Page 37

Optimization 1: Energy Spread

Minimize: Ratio of accelerated bunch length over ¼ plasma wavelength! Minimize length accele- rated bunch Increase plasma wavelength and/or Ultra-short bunches (fs, as) Ultra-fast science Lower plasma density Lower accelerating gradient Reduce energy spread (head to tail correlated with z) 1 fs = 0.3 μm when travelling with light velocity c

Ralph Aßmann | CAS | 27.11.2014 | Page 38

Phase Slippage

Drive beam (or laser) d

Ralph Aßmann | CAS | 27.11.2014 | Page 39

Phase Slippage

> Keep distance d constant for maximum acceleration and minimum energy spread. : Drive beam loses energy and (slightly) slows down. : Accelerated beam starts at low energy, gains energy and (slightly) speeds up. : Laser group velocity depends on plasma density and is slower than light velocity c.

Drive beam (or laser) d

Ralph Aßmann | CAS | 27.11.2014 | Page 40

Dephasing (β = v/c, here consider relativistic beams)

1e-10 1e-09 1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01 1012 1013 1014 1015 1016 1017 1018 1019 1020 1 - β Plasma density [cm-3] e- (5 MeV) e- (100 MeV) e- (1 GeV) e- (10 GeV) Plasma wave

Laser (815 nm) group velocity

Ralph Aßmann | CAS | 27.11.2014 | Page 41

Dephasing (β = v/c, here consider relativistic beams)

> Imagine . > Imagine . > After 1 m slippage by ≈10-5 m = . > Plasma wavelength: > However:

Driver electrons are decelerated and slow down. Accelerated electrons speed up.

> Big advantage of beam-driven…

1e-10 1e-09 1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01 1012 1013 1014 1015 1016 1017 1018 1019 1020 1 - β Plasma density [cm-3] e- (5 MeV) e- (100 MeV) e- (1 GeV) e- (10 GeV) Plasma wave

Laser (815 nm) group velocity

Ralph Aßmann | CAS | 27.11.2014 | Page 42

Dephasing (β = v/c, here consider relativistic beams)

> Imagine . > Imagine . > After 1 m slippage by ≈10-5 m = . > Plasma wavelength: > However:

Driver electrons are decelerated and slow down. Accelerated electrons speed up.

> Big advantage of beam-driven…

1e-10 1e-09 1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01 1012 1013 1014 1015 1016 1017 1018 1019 1020 1 - β Plasma density [cm-3] e- (5 MeV) e- (100 MeV) e- (1 GeV) e- (10 GeV) Plasma wave

Laser (815 nm) group velocity

3.6° - 360°

Ralph Aßmann | CAS | 27.11.2014 | Page 43

Optimization 2: Phase Slippage

Minimize: Phase slippage between driver and accelerated bunch Increase plasma wavelength Match velocity

• f driver to

accelerated beam and/or Many plasma stages (reset slippage to zero, …)

Lower plasma density Faster laser group velocity More tolerance

Ralph Aßmann | CAS | 27.11.2014 | Page 44

Optimization 3: Stability / Reproducibility

Stabilize: Distance between driver and accelerated bunch. Internally generate accelerated electron bunch Synchronize externally injected beam to driver Synchronize with for few degree phase stability

High accelera- ting fields

Drive beam (or laser) d

High plasma density

Ralph Aßmann | CAS | 27.11.2014 | Page 45

Maximum Acceleration

> (Beam 1) that pumps its energy into the plasma wakefield. (Beam 2) gets at > Energy conservation must be fulfilled: > From Estored,1 ≥ Estored,2 we find:

Ralph Aßmann | CAS | 27.11.2014 | Page 46

Maximum Acceleration > Would be great. E.g. take a 1 GeV electron drive beam with 1011 electrons to accelerate 109 electrons by 100 GeV! > This is, however, not possible in reality! > Limited by (short, symmetric bunches):

Here it is assumed, drive beam looses all its energy

Ralph Aßmann | CAS | 27.11.2014 | Page 47

Transformer Ratio (Short Symmetric Bunches)

Drive beam

T = 1 ?

Ralph Aßmann | CAS | 27.11.2014 | Page 48

Transformer Ratio (Short Symmetric Bunches)

Drive beam

T = 2 !

Ralph Aßmann | CAS | 27.11.2014 | Page 49

Record Acceleration: 42 GeV

E167 collaboration SLAC, UCLA, USC

• I. Blumenfeld et al, Nature 445,
• p. 741 (2007)

FACET: A National User Facility based on high-energy beams and their interaction with plasmas and lasers

• Facility hosts more than 150 users, 25 experiments
• One high profile result a year
• Priorities balanced between focused plasma

wakefield acceleration research and diverse user programs with ultra-high fields Slide: V. Yakimenko

High-Efficiency Acceleration of an Electron Bunch in a Plasma Wakefield Accelerator

• Electric field in plasma wake is loaded by presence of trailing bunch
• Allows efficient energy extraction from the plasma wake

Energetically Dispersed Beam After Plasma (Data)

Decelerated Drive Bunch

• x (mm)

y (mm) 5

• 5

15 20 5 10 25

Initial Energy Accelerated Trailing Bunch

This result is important for High Energy Physics applications that require very efficient high-gradient acceleration

• No Trailing

Bunch Trailing Bunch

Previous Experiments Our Experiment

Drive Bunch

Simulations Slide: V. Yakimenko

Ralph Aßmann | CAS | 27.11.2014 | Page 52

Increasing the Transformer Ratio

Ralph Aßmann | CAS | 27.11.2014 | Page 53

Physics of the Triangular Bunch Driver

(1) acts as precursor:

Gives plasma electrons an impulse so that they flow out of the beam driver region with an increasing flux. End of precursor: depletion rate

• f plasma electrons is balanced

by replacement rate of electrons in the drive bunch.

(2) :

Charge neutrality is maintained. Same decelerating field maintained.

(3) (sharp edge):

Plasma channel becomes non-neutral. Plasma electrons are strongly attracted back to the ions and large scale plasma

• scillations begin.

(1) (2) (3)

Ralph Aßmann | CAS | 27.11.2014 | Page 54

Alternative: Multi-bunch driven PWFA

Power et al, 2000

Ralph Aßmann | CAS | 27.11.2014 | Page 55

Optimization 4: Maximum Energy Gain

Maximize: Transformer ratio Shaping of driver bunch Respect energy conservation

• r

Driver beam should have high energy and/or high intensity or many bunches Modern photo- cathodes with bunch shape tuned through photo-cathode laser

Multiple bunch driver

Tolerances on timing, offsets, … Accelerated beam should have lower intensity Lower energy driver beams possible

Ralph Aßmann | CAS | 27.11.2014 | Page 56

The Non-Linear Regime

> Blow-out and Non-Linear Regime > Wave-Breaking as Limit to Maximum Energy Gain > Self-injection in wave-breaking regime > Hybrid Schemes Trojan Horse

Ralph Aßmann | CAS | 27.11.2014 | Page 57

Blow-Out Regime Equilibrium condition: n r n0 Drive beam Ion channel Quasineutral plasma an

(neutralization radius) Ion charge neutralizes beam charge:

n n a

b r n

⋅ =σ

Beam size Beam and plasma densities determine most characteristics of plasma wakefields!

SLC: nb/n0 = 10

Ralph Aßmann | CAS | 27.11.2014 | Page 58

Fields Calculated with OSIRIS Code: Non-Linear Regime

50 100 150 200 250 300

• 0.4
• 0.2

0.2 0.4

Longitudinal field Transverse field x10

• 3

cm

17

Plasma density 10

20 40 60 80 100 120 140

• 3

cm

18

Plasma density 10

• 1
• 0.5

0.5 1

z [μm] Wz,x / Wz,0

Wz,0 = 30.4 GV/m Wz,0 = 96 GV/m

Ralph Aßmann | CAS | 27.11.2014 | Page 59

Plasma Accelerator Physics I

> A plasma of density n0 (same density electrons - ions) is characterized by the : > This translates into a

• f the plasma oscillation:

> The wavelength gives the longitudinal size of the plasma cavity… Lower plasma density is good: larger dimensions. 0.3 mm for n0 = 1016 cm-3

Ralph Aßmann | CAS | 27.11.2014 | Page 60

Plasma Accelerator Physics II

> The plasma oscillation leads to with a gradient of (higher plasma densities are better): > The is as follows for ωp << ωl: (note ωl is laser frequency) > The laser-driven wakefield has a lower velocity than a fully relativistic electron slippage and dephasing. Lower densities are better. 9.6 GV/m for 1016 cm-3

∝ N b

z

σ 2

Ralph Aßmann | CAS | 27.11.2014 | Page 61

Plasma Accelerator Physics III

> The ion channel left on axis, where the beam passes, induces an . In the simplest case: > This can be converted into a (lower density is better , as beta function is larger):: > The in the plasma channel is rapid: 300 kT/m for 1016 cm-3 β = 1.1 mm for 100 MeV

Ralph Aßmann | CAS | 27.11.2014 | Page 62

Plasma Accelerator Physics IV

> The in the ion channel is small: > Offsets between laser and beam centres will induce betatron

• scillations. Assume: full dilution into emittance growth (energy spread

and high phase advance). > Tolerances for due to offsets Δx = σx: > Lower plasma density better: larger matched beam size, bigger tolerances. σ0 = 1.3 μm for γε = 0.3 μm 100% for 1.3 μm offset

Assmann, R. and K. Yokoya. Transverse Beam Dynamics in Plasmas. NIM A410 (1998) 544-548.

Ralph Aßmann | CAS | 27.11.2014 | Page 63

Makes Things Difficult…

> Conventional acceleration structures:

Optimized to provide longitudinal acceleration and no transverse forces on the beam. Due to imperfections, transverse forces can be induced. These wakefields caused major trouble to the first and only linear collider at SLAC.

> Plasma acceleration:

Ultra-strong longitudinal fields high accelerating gradient. Ultra-strong transverse fields transverse forces cannot be avoided and must be controlled.

> For fun: A look at the SLAC linac beam before entering the plasma!

Ralph Aßmann | CAS | 27.11.2014 | Page 64

Seeing Electron Beam… 1.8 mm The transverse and longitudinally fields of the accelerator are set up to achieved small transverse beam sizes (right).

~ 2e10 electrons, 30 GeV

100 200 300 400 500 600 2 4 6 8 10 12 14

Plasma OFF Plasma ON Envelope

σx (μm) Ψ L=1.4 m σ0=14 μm εN=18×10-5 m-rad β0=6.1 cm α0=-0.6

• Smaller matched beam size at the plasma entrance reduces amplitude of the betatron
• scillations measured at the OTR downstream of the plasma
• Allows stable propagation through long plasmas (> 1 meter )

50 100 150 200 250 300

• 2

2 4 6 8 10 12

σX DS OTR (μm) ψ=K*L∝ne

1/2L

σ0 Plasma Entrance=50 μm εN=12×10-5 (m rad) β0=1.16m

E-157 E-162 Run 2

Beam Propagation Through A Long Plasma

• C. E. Clayton et al., PRL 1/2002

Phase Advance Ψ ∝ ne

1/2L Plasma OFF

Phase Advance Ψ ∝ ne

1/2L

sx (µm)

UCLA

E-157/E-162 collaboration

• R. Assmann

66

Ralph Aßmann | CAS | 27.11.2014 | Page 67

Wave Breaking

Water velocity becomes larger than phase velocity of the wave Dawson 1959: if plasma modeled with one-dimensional sheets, then wave breaking equivalent to crossing of neighboring sheets.

Ralph Aßmann | CAS | 27.11.2014 | Page 68

Wavebreaking Limit > Dawson 1959: if plasma modeled with one-dimensional sheets, then . > Non-relativistic wavebreaking field E0:

Ralph Aßmann | CAS | 27.11.2014 | Page 69

Wave Breaking in Plasma Wakefields

> Relativistic wavebreaking: . > Relativistic wavebreaking field ( ): > Thermal electron effects lead to reduction in wavebreaking field. Physics: A large fraction of the electron distribution will become trapped in the plasma wave wave breaks.

Ralph Aßmann | CAS | 27.11.2014 | Page 70

Trapped in the Breaking Wave

Ralph Aßmann | CAS | 27.11.2014 | Page 71

Using the Trapped Electrons

Pukhov, ter-Vehn 2002

See lecture of Alexander Pukhov

72 72 Office of Science

4.25 GeV beams have been obtained from 9 cm plasma channel powered by 310 TW laser pulses (15 J)

Angle (mrad) Electron beam spectrum 1 2 3 4 5 Beam energy [GeV]

• simulation*

Exp. Sim. Energy 4.25 GeV 4.5 GeV ΔE/E 5% 3.2% Charge ~20 pC 23 pC Divergence 0.3 mrad 0.6 mrad

• Slide: W. Leemans

Ralph Aßmann | CAS | 27.11.2014 | Page 73

Bringing in the Trojan Horse

Ralph Aßmann | CAS | 27.11.2014 | Page 74

The Hybrid Scheme (Trojan Horse)

He electrons are released with low transverse momentum in the focus of the copropagating, non-relativistic intensity laser pulse directly inside the accelerating or focusing phase of the Li blowout generation of sub-μm- size, ultralow-emittance, highly tunable electron bunches.

Beam-driven plasma wakefield acceleration using low-ionization- threshold gas such as Li Laser-controlled electron injection via ionization of high-ionization- threshold gas such as He.

Ralph Aßmann | CAS | 27.11.2014 | Page 75

Sketch (Hidding et al, 2012)

Ralph Aßmann | CAS | 27.11.2014 | Page 76

Sketch (Hidding et al, 2012)

Other approaches being studied, e.g. injection on the plasma density ramp

Ralph Aßmann | CAS | 27.11.2014 | Page 77

Tolerances and Towards Plasma Accelerators

Ralph Aßmann | CAS | 27.11.2014 | Page 78

• Energy-spread growth
• Reason: slope in the accelerating field

in the focusing part of the plasma cavity

• Solution: accelerate bunches which
• ccupy only a small fraction of the

plasma wavelength

• Emittance growth (inside plasma)
• Reason: mismatch of the bunch Twiss

parameters to the intrinsic plasma beta

• Solution: precise transport and

matching of the bunch inside plasma

• Emittance growth (after plasma)
• Reason: chromatic effects due to the

energy spread

• Solution: minimise energy spread

Beam Dynamics in Plasma Acceleration (J. Grebenyuk, RA)

Ralph Aßmann | CAS | 27.11.2014 | Page 79

Energy + Energy Spread after ≈ 1 cm Plasma

n0 = 1017 cm-3 20 fs

Ralph Aßmann | CAS | 27.11.2014 | Page 80

Beam Loading to Flatten Wakefield S. van der Meer – T. Katsouleas

> Idea: Simon van der Meer – CLIC Note No. 3, CERN/ PS/85-65 (AA) (1985). > Shape the electron beam to get optimized fields in the plasma, e.g. minimize energy spread. > Study: Tom Katsouleas.

Katsouleas, T., et al. Beam Loading in Plasma

• Accelerators. Particle Accelerators, 1987, Vol. 22,
• pp. 81-99 (1987)

This case we simulated. Other cases to come.

Ralph Aßmann | CAS | 27.11.2014 | Page 81

Injection Tolerance: Beam to Plasma Wakefield

> A tolerance for doubling of the initial emittance is calculated. > Assumptions:

δ = 0.1% Full dilution

> Injection tolerances for the considered SINBAD case (100 MeV):

0.01 0.1 1 10 100 1012 1013 1014 1015 1016 1017 1018 1019 1020 Injection tolerance [μm] Plasma density [cm-3] REGAE SINBAD

Center laser Center beam Injection tolerance Plasma

Ralph Aßmann | CAS | 27.11.2014 | Page 82

Emittance Growth I

Ralph Aßmann | CAS | 27.11.2014 | Page 83

Emittance Growth II

Ralph Aßmann | CAS | 27.11.2014 | Page 84

Emittance Growth III

Ralph Aßmann | CAS | 27.11.2014 | Page 85

Emittance Growth IV

Ralph Aßmann | CAS | 27.11.2014 | Page 86

Accelerator Builder’s Challenge (simplified to typical values) > Match into/out of plasma with (about 1 mm beta function). Adiabatic matching (Whittum, 1989). > Control between the wakefield driver (laser or beam) and the accelerated electron bunch at . > Use to minimize energy spread. > Achieve from injected electron bunch to wakefield (energy stability and spread). > Control the to compensate energy spread (idea Simon van der Meer). > Develop and demonstrate .

Ralph Aßmann | CAS | 27.11.2014 | Page 87

Relax conditions…

> As low as possible plasma densities to start in most simple

• conditions. Larger matched beam size, relaxed tolerances,

… > The success will be all in accuracy, tolerances, precision! We mastered this in conventional accelerators. > Do the same for plasma accelerators!

Ralph Aßmann | CAS | 27.11.2014 | Page 88

Accelerator Builder’s Challenge – Feasible?

> Difficult but we believe solutions can be found. Will not come for free…

50 nm with a 1.3 GeV electron beam

(from K. Kubo et al.

• Proc. IPAC 2014)

Ralph Aßmann | CAS | 27.11.2014 | Page 89

Accelerator Builder’s Challenge – Feasible?

> Difficult but we believe solutions can be found. Will not come for free… > Again: No fundamental limit here, but strong technical challenges!

Femtosecond Precision in Laser-to-RF Phase Detection

(from H. Schlarb, T. Lamb, E. Janas et al. Report on DESY Highlights 2013).

Ralph Aßmann | CAS | 27.11.2014 | Page 90

Livingston and Accelerators at the Energy Frontier

Ralph Aßmann | CAS | 27.11.2014 | Page 91

Livingston and Accelerators at the Energy Frontier Shows potential of plasma acceleration for very high energies

Ralph Aßmann | CAS | 27.11.2014 | Page 92

Livingston and Accelerators at the Energy Frontier Shows potential of plasma acceleration for very high energies Plasma acc. today in regime required for FEL’s

• !

Ralph Aßmann | CAS | 27.11.2014 | Page 93

Livingston and Accelerators at the Energy Frontier

Advent of plasma acc.:

• 1. Metallic cavity walls replaced with

plasma walls overcoming hard physical limits of metallic RF structures.

• 2. Acceleration lengths (same energy) are

factor 100 – 1000 shorter. Multi-GeV e- beams proven.

• 3. Still short-comings but no fundamental

limit.

Ralph Aßmann | CAS | 27.11.2014 | Page 94

Small is Beautiful!? Is it?

Ralph Aßmann | CAS | 27.11.2014 | Page 95

Wideröe 1992 at age 90

After all, . are not subject to any such considerations. The . The with regard to accelerating particles by electromagnetic means (i.e. within the scope

• f the Maxwell equations which have been known since

the 19th century), , and technology surprises us almost daily with innovations which in turn allow us to broach new trains of thought. …there are yet to be made. They could allow us to advance to .

Ralph Aßmann | CAS | 27.11.2014 | Page 96

Thank you for your attention…