possibility of narrow-band thz csr by means of transient h/l coupling newsubaru, lasti, university...

Possibility of narrow-band THz CSR by means of transient

H/L coupling

NewSUBARU, LASTI,University of HyogoY. Shoji

1 Landau damping by the chromaticity modulation

;T. Nakamura, et al., IPAC’10

2 Coherent Synchrotron Radiation (CSR) from wavy bunch

; Y. Shoji, Phys. Rev. ST-AB13 060702 (2010)

3 Transient H/L coupling

; Y. Shoji, NIMA in press (available on-line)

; 2010 日本物理学会4 Possibility of CSR emission by means of the coupling

New Idea !

Today’s Lines

Suppose that particles in a bunch have tune variation (spread).

After many revolutions, they oscillate with different phases.

Then the oscillation amplitude of the average (coherent osci.) becomes smaller.

start time

Landau damping of betatron motiondi

spla

cem

ent

Suppose that particles in a bunch have tune variation (spread).

After many revolutions, they oscillate with different phases.

Then the oscillation amplitude of the average (coherent osci.) becomes smaller.

start time

Landau damping of betatron motiondi

spla

cem

ent

It suppresses the growth of the oscillation.

suppression of any transverse instability

Chromatic Tune Spread 　

Betatron tune shift with chromaticity

With synchrotron oscillation

Averaged tune shift over TS

δ =δ0 cosωSt + (ωS / α P )τ 0 sinωSt

€

Δν =ξ0 δ






δ =0.047%

ξ0 = 5

ξ1 = 0

time (ms)

Coh

eren

t osc

illa

tion

am

plit

ude

TS = 0.2 ms

€

Δν =ξ0 δ






δ =0.047%

ξ0 = 5

ξ1 = 0

time (ms)

Coh

eren

t osc

illa

tion

am

plit

ude

TS = 0.2 ms


Chromaticity modulation




time (ms)

δ =0.047%

ξ0 = 0

ξ1 = 1

Coh

eren

t osc

illa

tion

am

plit

ude

TS = 0.2 ms

ΔνTS

= ξδTS

=1

2ξ1δ 0

tune spread

€

Δν = ξ0 + ξ1 cosωS t( )δ


Chromaticity modulation




time (ms)

δ =0.047%

ξ0 = 0

ξ1 = 1

Coh

eren

t osc

illa

tion

am

plit

ude

TS = 0.2 ms

ΔνTS

= ξδTS

=1

2ξ1δ 0

Generation of spatial wavy bunch

The wavy structure is instantaneously produced.

Its wave number increases with time.

Is there any way to utilize this structure?

ExelectronzbunchExelectronzbunchExelectronz

CSR

非 CSR

CSR

放射パワー :P

バンチ内電子数 :N

single bunch 1mA

N=2.5 x109electrons

€

P ∝N

€

P ∝N 2

Radiation from N electrons in a bunch

Form factor ; f

€

PTOTAL (ω)∝ p(ω)[N + (N 2 − N) f (ω)2]

€

f (ω) = ρ (z)∫ Exp(iωz /c)dz

Coherent Synchrotron Radiation (CSR)

Modulation and Radiation

No modulation

Spatial modulation

Density modulation

Vertical spatial modulation--> Vertically polarized radiation

xyExzyEyzExzExelectron bunchz

Coherent Synchrotron Radiation (CSR)


0

0.2

0.4

0.6

0.8

1

1.2

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30 35 40

Frequency (THz)

Phase shift spread (radian)

time ( π/ω s )

ω ψ C /2 π

( ω S / π ) t C

Transverse coherent oscillation is damped by the longitudinal radiation excitation with finite chromaticity(Is this a Landau damping?)


0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Intensity

(arb.unit)

Frequency (THz)

H; longitudinal structure

V; vertical structure

0

0.5

1

1.5

0 20 40 60 80 100

Intensity (arb.unit)

y (mm)

H; incoherent X10

V; incoherent X10

H; CSR

V; CSR

6

6

Power spectrum of CSR at n=22 (t=22π/ωS) andθ0=0.Spatial intensity distribution along y-direction at n=22 (t=22π/ωS) forωψ≈2π×0.68 THz.

H/L coupling can produce CSR

Is it really impossible to generate CSR by horizontal deflection?

Horizontal kick + Chromaticity modulation

Horizontal spatial wavy structure

At dispersive locations

Longitudinal wavy structure

= Density modulation

CSR

Horizontal kick also works to generate CSR!

Transient H/L coupling

A particle circulating around a ring with horizontal betatron motion

runs inner side and outer side of bending magnets

Transient longitudinal oscillation

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 2 4 6 8 10 12

betatron oscillation

s

Bend BendBendBend

Δ L > 0 Δ L > 0Δ L < 0 Δ L = 0

€

ΔL(s) =x

ρs0

s

∫ ds

€

x(s) = ε0β cosψ

Transient H/L coupling 　

A particle circulating around a ring with horizontal betatron motion

runs inner side and outer side of bending magnets

Transient longitudinal oscillation

Simple analytical formulae [Y.Shoji, PR ST-AB7 090703(2004)]

Longitudinal movement after the deflection [Y.Shoji, NIMA in press]

€

x = ε0β cosψ

€

x'= ε0γ cos(ψ +ψG )

€

z = ε0H cos(ψ +ψ H )

€

z2 = ε CSI H 2 cos(Δψ 21 +ψ1 +ψ H 2 )− ε CSI H1 cos(ψ1 +ψ H1)

H/L coupling can produce CSR

Stored electron energy 0.5 GeVp 0.0013Revolution frequency 2525 kHzNatural energy spread 0.024 %L damping time 96 msfs 15 kHzAC chromaticity amp 10Natural emittance7.5 nmH at the observation point 0.2 mHorizontal deflection 150 nm

t = 6.5 Ts

Measurement at NS – Not yet started

Non-achromatic lattice

(Y. Shoji, 2005 Ann. Meeting of PASJ)

Electron energy 1 GeV

Dispersion at AC6 0.73 m

Beta func. at AC6 17/13 m

Betatron tune 6.2, 2.2

DC chromaticity 33

Synch. osc. frequency 5 kHz

Natural energy spread 0.047%

Rad. damping time 22 ms

0

10

20

30

40

50

-0.5

0

0.5

1

1.5

2

051015202530Beta function

βH, βV[ ]m Dispersion

η [ ]m

( )s m

βH

βV

η

AC6

AC Sextupole magnet system( T. Nakamura, K. Kumagai, Y. Shoji, T. Ohshima, … MT-20, 2007)

Pole length 0.15m

Bore diameter 80 mm

Yoke material 0.35 mm Si steel

Coil turn 1 turn/pole

Operation frequency 4 – 6 kHz

Drive current 300A peak

Field strength 36 T/m2

Modulation amplitude ξ11.63/1.25

Damping time 0.21/0.27 ms

(Synchrotron osci. period 0.2ms)

Now trying to reduce Eddy-current loss at the inner coil


Coherent Oscillation Damping single kick sinusoidal deflection

H / V

ξ0 =1.1 / 0.9

L = 1.3 / 1.6 ms

L =0.84 / 1.1 ms

L =0.42 / 0.54 ms

ξ1 =0.82 / 0.63 ms

RAD =22 ms; Ts=0.2 ms


Multi-function Corrector Magnet System( Y. Shoji, … MT-21, 2009, IPAC’10)

Can afford to produce Skew quadrupole Skew sextupole Normal octupole

4 magnets at the dispersion sections2 magnets at the straight section


CLOSING COMMENT

We are preparing for the demonstration, but not yet started.

We hope someone, who is interested in, will come to join us.

Thank you for your attention.

possibility of narrow-band thz csr by means of transient h/l coupling newsubaru, lasti, university...

Documents

ms tune

chromatic tune

betatron tune shift

t s slide

t s time ms

ms slide

shoji slide

time landau