LCLS-II longitudinal space charge (LSC) simulations and

sub-fs x-ray pulse generation

Y. Ding, Z. Huang and J. Wu

11.16.2011

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outline

LCLS-II LSC check LCLS-II optics: bypass line 250pC, 4.2/13.5 GeV, LH = 20keV 20 pC, 4.2/7/13.5 GeV, LH off

sub-fs hard x-ray pulse generation 20 pC, 13.6 GeV, LCLS-I, LH off

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LCLS-II optics (Jan 2011 beamline setup for CDR)

1km bypass 3

Longitudinal space charge force

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2

20 1ln24

)()V/m(

bb

zz

r

r

r

sIZE

)(

)distance(

/1 2

sI

L

LSC results in energy modulation, which will further convert to density

modulation (micro-structure), and increase final energy spread .

We used a smooth initial distribution with 10 M particles at 135 MeV,

dumped from IMPACT-T simulations.

In Elegant simulations, 250 pC, LSC bin=2000; 20 pC, LSC bin=500.

It is not easy to quantify the LSC effect. We show some LCLS-I simulation

examples to compare.

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250pC, 13.5 GeVLI20 END Bypass END

UND BEG

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250pC, 4.2 GeVLI20 END Bypass END

UND BEG

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A reference from LCLS-I, @ UND BEG

13.6 GeV 4.3 GeV

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20 pC, 13.5 GeV, LH off BC2END LI20 END

Bypass END UND BEG

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20 pC, 13.5GeV, ~ 2kA

BC2END UNDBEG

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20 pC, 7 GeV, 2 kABC2END LI20END

Bypass END UNDBEG

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20 pC, 7 GeV, 2 kA

BC2END UNDBEG

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20 pC, 4.2 GeV, ~ 2kA, LH offBC2END LI20END

Bypass END UNDBEG

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20 pC, 4.2GeV, 2kA

BC2END UND BEG

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Intentionally turn off LSC, 20pC,4.2 GeV

BC2 END LI20 END

UND BEG

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To compare, an example of LCLS-I, 20 pC, 4.3 GeV, LH off

@ undulator entrance

@ L3 END

DL2

FEL works.

DL2 R56 = 0.13mm

DL2 R56 = 0 mm

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If LH can work to increase energy spread to 5 keV…

Bypass end UND BEG

Slice energy spread for the core part is about 1.4 MeV. 16

Sub-fs hard x-ray pulse generation

“ESASE” without laser modulation

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Elegant simulations based on LCLS-I

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BC2END

Initial condition:

20 pC.bunch length=270um rms at OTR2;Energy spread < 1keV rms;Laser heater off.

Used 10 M particles in Elelgant.

DL2 R56 =0.13 mm.

Check LSC in L3, 20pC, 13.6 GeVL3END UNDBEG

LSC off in L3

DL2 R56 =0.13 mm

L3END

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20pC, DL2 R56 = 0.13mm

Undulator entranceWake loss from LSC in undulator

resistive wall wake loss from undulator chamber

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LSC induced energy loss

At Undulator entrance At Undulator z=95m, taper = -0.5% over 80m

•For 20pC DL2=0.13mm case, the LSC wake is much larger that resistive wall wake loss inside undulator. We only include the LSC loss in Genesis simulations.

•A chirp is induced in the double horns due to the LSC.

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How does chirp + negative taper work for FEL?

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2

20

Kur

• FEL works at resonance condition: electrons wiggle one period λu, radiation slips by one wavelength λr.

• Small energy chirp with constant undulator K could produce frequency-chirped radiation.

• Each slice of the energy chirped bunch will generate radiation at a different frequency along the tapered undulator, and the frequency is equal to the radiation from the slice behind at an previous undulator location. Same frequency radiation will overlap after slippage.

λr

z

x λuK

x

λr

z

K

Genesis results, DL2 0.13mm, LSC included in undulator, No taper

60m (HXRSS location)

75m

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Genesis results, DL2 0.13mm, LSC included in undulator, taper: -0.2% over 80m

60m

75m 90m

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Genesis results, DL2 0.13mm, LSC included in undulator, taper: -0.5% over 80m

60m

75m 90m

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Genesis results, DL2 0.13mm, LSC included in undulator, taper: -0.8% over 80m

60m

75m 90m

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Genesis results, DL2 0.13mm, LSC included in undulator, taper: -1% over 80m

60m

75m 90m

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LCLS-I undulator taper range is good

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-0.5% over 80m

How to test this at LCLS?

1) Using slotted foil, horizontal scan

2) using spectrometer, spoil one of the spikes.

We can also suppress double horns using zero or negative DL2 R56, e.g., for HXRSS

DL2, R56 = 0.13mm DL2, R56 = 0.0

@UND BEG @UND BEG

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Discussions

LSC should not be a problem for LCLS-II nominal charge (150-250 pC) with

laser heater on, but for low charge such as 20 pC with laser heater off, it can

affect the bunch temporal profile, especially at very low beam energy; Laser heater helps to reduce the LSC effects. But for low charge operation,

we only need a small heating (about 5 keV), and trickle heating problem

prevents working on this low level; On the other hand, at high energy, we can take advantage of the LSC to fully

suppress the beam in the double-horn region, and achieve narrow spikes with

very high current, like ESASE; With the help of a negative undulator taper, it is possible to make the double-

horn lase only, hence to produce very short x-ray pulses below fs. It only works

at hard x-ray wavelength. This can be tested at LCLS-I.

Longitudinal space charge can be further studied using Impact-z, if needed.

Billion particles are preferred.

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