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Influence of a Space Charge Effect in aFemtosecond Electron Beam on Coherent

Transition Radiation Spectrum

M. Shevelev1, A. Aryshev1, Y. Honda1,2, N. Terunuma1,2 andJ. Urakawa1

1High Energy Accelerator Research Organization (KEK)

2The Graduate University for Advanced Studies (SOKENDAI)

Tsukuba, Ibaraki, 305− 0801, Japan

30 September 2016

2/22

Motivations and goals

Top Goal:

I Development of radiation source based on compactaccelerator.

Subgoals:

1 estimation of bunch length in experimental area using ASTRAsoftware for usual settings of LUCX facility;

2 optimization of LUCX parameters for suppression of spacecharge effect;

3 demonstration how the beam dynamics could influence oncoherent radiation of electron bunches.

3/22

Report outline:

1 ASTRA simulation;

2 Experimental test;

3 Discussions and conclusion.

4/22

ASTRA

ASTRA - A Space Charge Tracking Algorithm written by KlausFlottmann from DESY (Germany)1.

The software allows tracking charge particles bunches throughdifferent beam line components. Plus it permits to take intoaccount space charge effect.

1K. Flottmann ASTRA (DESY, Zeuthen, 2013)

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LUCX facility and controlled settings

RF Gun

Solenoid

GVGV

ScreenT z ChamberH

laser pulse

ICT FCT

1.31m

1.72 m

x

y z

We could change the next parametersin real experiment:

I solenoid current;

I bunch charge (from a darkcurrent to 400 pC);

I maximum value of an electricfield strength on the cathode(from 60 to 120 MV/m);

I laser spot size on the cathode(from 340× 420 µm2 to severalmm);

I laser pulse duration (from 50 to200 fs);

I laser pulse energy.

6/22

Electron distributions in bunch

Transverse distributionLongitudinal distribution

Simulation parameters: laser pulse is 100 fs, laser spot size is 450× 450 µm2,

Q = 25 pC, MaxB= 0.225 T, MaxE= 77 MV/m, z = 1.31 m.

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Solenoid scan

0.210 0.215 0.220 0.225 0.230 0.235 0.240

Maximum value of magnetic field in the solenoid (T)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Tran

sver

sesi

ze(m

m)

200

400

600

800

1000

1200

1400

long

itudi

nals

ize

(fs)

σx

σy

σz

Simulation parameters: Q=25 pC, t=100 fs, σlx = σl

y = 0.45 mm,

MaxE=80 MV/m, RF gun phase= 30deg., z = 1.72 m.

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Charge scan

0 50 100 150 200

Bunch charge (pC)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Tran

sver

sesi

ze(m

m)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

long

itudi

nals

ize

(ps)

σx

σy

σz

Simulation parameters: MaxB=0.233, t=100 fs, σlx = σl

y = 0.45 mm,

MaxE=80 MV/m, RF gun phase= 30 deg., z = 1.31 m.

9/22

Charge scan for different value of maximum amplitude ofelectric field strength on the cathode

0 50 100 150 200

Bunch Charge (pC)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5Lo

ngitu

dina

lsiz

e(p

s)

60 MV/m80 MV/m100 MV/m120 MV/m

Simulation parameters: MaxB=0.2254, t=100 fs, σlx = σl

y = 0.45 mm,

MaxE=80 MV/m, RF gun phase= 30 deg., z = 1.31 m.

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Laser settings

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Laser spot size on the cathode (mm)

0.0

0.5

1.0

1.5

2.0

Long

itudi

nals

ize

(ps)

60 MV/m80 MV/m100 MV/m120 MV/m

50 100 150 200

Laser pulse duration (fs)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Long

itudi

nals

ize

(ps)

Simulation parameters: Q=25 pC, MaxB=0.2254, t=100 fs,

σlx = σl

y = 0.45 mm, MaxE=80 MV/m, RF gun phase= 30 deg., z = 1.31 m.

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Simulation summary

A Magnetic field in solenoid allows compensate transverse sizeof electron bunches without any effects on longitudinal size;

B Increase of bunch charge using laser technique would increasethe space charge forces in bunch;

C The laser pulse length does not influence on bunch length (inreasonable range);

D Transform laser spot size on the photocathode we couldsuppress space charge effect in electron bunches.

Let’s check!

12/22

Experimental scheme and electron beam settings

RF Gun

Accel. M

Soleniod

Laser pulse

Screen

M2

M1

BS

PM

Detector

Beam direction

Sapphirewindow

Traget

PMPM

Electron beam parameters:

I One bunch operation mode;

I Beam energy (RF gun out) is7.9 MeV ⇒ maximum value ofelectric field strength on thecathode (MaxE) is 80 MV/m ;

I Transverse electron beam size onthe luminophore screen is 230 µm(gauss distribution);

I Bunch charge iss 60 pC which ismeasured by FCT.

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Form-Factor for coherent transition radiation

Coherent Transition Radiation:

d2WCTR

dωdΩ=

[N +N (N − 1)F 2 (k)

] d2WTR

dωdΩ, (1)

where F (k) is the form-factor. Formfactor for transition radiationwas calculated analytically2:

F (k) = F (λ, θ, η, ψ)

= exp

[− 2π2

λ2

(σ2x

(tan θ

β− cosψ (cos η tan θ + sin η)

)2

+ σ2y sin2 ψ cos2 (η − θ) +σ2zβ2

)],

where is λ the wavelength, θ is angle of incidence, η is the angle ofobservation, ψ is the azimuth angle of observation.

2G. Naumenko Adv. Material Res. 1084 (2015) or A. Potylitsyn JETP Lett.103 (2016)

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Orientation dependence of TR

40 45 50 55

θ (deg)

0.5

1.0

1.5

2.0

2.5

3.0

Inte

nsity

(arb

.uni

ts)

−10 −8 −6 −4 −2 0 2 4

φ (deg)

4.5 5.0 5.5 6.0 6.5 7.0 7.5

Distance (mm)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Inte

nsity

(arb

.uni

ts)

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Laser spot size on the virtual cathode

11.0 11.5 12.0 12.5 13.0 13.5 14.0

Revative distance (mm)

300

400

500

600

700

800

900

UV

lase

rspo

tsiz

e(µ

m)

σly

σlx

Relative distance is 12 mm

Relative distance is 13.5 mm

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Laser spot size scan

11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5

Revative distance (mm)

3

4

5

6

7

Inte

nsity

(arb

.uni

ts)

4.5 5.0 5.5 6.0 6.5 7.0 7.5

Distance (mm)

2

3

4

5

6

7

8

Inte

nsity

(arb

.uni

ts)

0.5

1.0

1.5

2.0

2.5

3.0

Inte

nsity

(arb

.uni

ts)

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Charge scan: comparison between experimental data andsimulation results

Relative distance is 12 mm

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Bunch charge (nC)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5In

tens

ity(a

rb.u

nits

)

−0.84 + 29.70 · x0.64

−0.84 + 23.95 · x0.57

Experimantal dataSimulations

Simulation parameters: Q=60 pC, MaxB=0.2335, t=100 fs, σlx = 344.91 µm,

σly = 420.50 µm, MaxE=80 MV/m, RF gun phase= 30 deg., z = 1.31 m.

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Fit function: y = a+ bc.Simulations:

Parameter Estimation Standard Error

a −0.84 0.34b 29.7 7.83c 0.64 0.10

Experimental data:

Parameter Estimation Standard Error

a −0.84 0.34b 23.95 6.22c 0.57 0.10

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Charge scan

Relative distance is 13.5 mm

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Bunch charge (nC)

0

1

2

3

4

5

6

7

8

Inte

nsity

(arb

.uni

ts)

−0.55 + 66.92 · x0.77

−0.46 + 71.40 · x0.79

Experimantal dataSimulation

Simulation parameters: Q=60 pC, MaxB=0.228, t=100 fs, σlx = 727.42 µm,

σly = 0.757.21 µm, MaxE=80 MV/m, RF gun phase= 30 deg., z = 1.31 m.

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Fit function: y = a+ bc.Simulations:

Parameter Estimation Standard Error

a −0.55 0.47b 66.92 10.55c 0.77 0.08

Experimental data:

Parameter Estimation Standard Error

a −0.46 0.19b 71.40 5.66c 0.79 0.04

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Conclusion future plans

Conclusions:

I ASTRA software allows to estimate the bunch parameters forour experimental conditions;

I In the case of LUCX facility, the space charge effect is themain barrier to produce intense radiation source in THz range;

I Laser technique is not suitable to confirm quadraticdependence of coherent radiation intensity;

I However, laser techniques allows to suppress space chargeeffect in femtosecond electron bunches.

Future plans:

I We are going to decrease space charge effect in the RF gunusing spatial reshaping technique for laser pulse;

I We make optimization of the LUCX settings for themulti-bunches operation mode (two and four bunches).

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Thank you for attention!