Phase-space rotation technique and applications Masao KURIKI Hiroshima University International School on Electron Accelerator, Free Electron Laser and Application of Electron Beam and THz radiation 6-9, March, 218, IUAC, Dehli, India
Content Introduction Emittance Exchange Applications. Summary
Introduction Area of the phase-space occupied by particles: emittance. In principle, the emittance is the volume in 6D phase-space. The 6D emittance is invariant (Loisville's theorem). z px py pz ｘ ｙ ｘ px
Louisville's theorem 6D emittance is invariant. 2D emittance (ex, ey, ez) can be conserved, but not invariant. Can the partitioning of x, y, and z be modified as we want? (Phase-space rotation). Emittance No coupling With coupling ex ey ez conserved convserved conserved varied varied varied ex*ey*ez Invariant Invarian
XY-Z Emittance Exchange TLEX (Transverse to Longitudinal Emittance exchange)
XY-Z Emittance Exchange TLEX TLEX can be made with chicane or two doglegs and a dipole mode RF cavity. The phase spaces of X(transverse direction in def lecting plane) and Z (longitudinal direction) are swapped.
Transfer Matrix One dog-leg section Dispersion Momentum compaction Effective length [ ] 1 L 1 M D (η, ξ, L )= η η ξ 1 1 ( sin α 2D 1 η=s 1 2 + 1 cos α sin α cos α sin 2 α 2D ξ=s 1 3 + cos α sin α α 1 2D L=S 1 3 + +S 2 cos α cos α )
Transfere Matrix of Diple RF TM11cavity [ ] 1 M C= k 1 k 1 1 V k= ae By/B Ez/E
Matrices -EEX section- M EEX =M D (η, ξ, L ) M C M D (η, ξ, L ) [ L/η η L ξ /η 1/η ξ /η = ξ /η η L ξ/ η L 1/ η η matching condition ] x 1+ηk = z1 compression factor dilution factor ξ ξ z 1= η x +(η L η ) x ' x-z space exchange 1 L by the 4D space rotation. δ1 = η x η x ' otsuki
Tunable Subpicosecond Electron-BunchTrain Generation Using a Transverse-ToLongitudinal Phase-Space Exchange Technique Y.-E Sun, et al., PRL(15)23481(21)
Primary modulation (slits in x) After Z-X rotation (y corresponds to z) RMS<3fs (limited by resolution)
XY Emittance Exchange RFTB(Round to Flat Beam Transformation)
Magnetized Beam Beam Generation in solenoid f ield (Bz) Canonical momentum by Vector potential has the angular momentum. By the fringe f ield, the canonical momentum becomes the kinetic momentum. The x-py and y-px correlated beam is obtained. Vector Potential B A y= x 2 B A x = y 2 Magnetized Beam e A P c = P P c In sigma matrix [ 1 κ2 2 Σ =σ κ κ κ κ 1 κ2 ] κ eb 2mc eb o y 2 x ( )
Restoration Matrix By ignoring the intrinsic emittance, the beam at the exit of the solenoid f ield is (x and y are correlated.) Beam transfer with a matrix M is ( )( Y = S X X 1 M 11 = Y1 M 21 S= ( ) 2 eb eb 2 )( ) ( ) M 12 X 1 =M X S M 22 Y If the condition is satisf ied, Y1 is independent from X. The correlation is restored. M 21+ M 22 S = E. Thrane, LINAC22
How to restore? Sigma matrix at the downstream of solenoid field. Σ= ( ϵt c LJ T = M should vanish the nondiagonal component (LJ) of the sigma matrix. LJ ϵt ( β ) α 1+α β α [ 2 eb σ c L= pz ) ϵ- T Σ= M Σ M = ϵ+ T + J= ] ( 1 1 )
M matrix Let us assume three skew Qs M =R 1 Q (q3 )O ( D)Q (q 2)O ( D)Q(q1) R ( 1 A+ A= 2 A- A+ Assume ) A - = A+ S To satisfy [ R= ( 1 I 2 I =R 1 N Q R I I ) ( N Q= A B ) A+- = A± B M= ( 1 A+ 2 A+ S ϵ- T Σ= M Σ M = ϵ+ T + ] A+ S A+ ) [ α β 2 S =±JT 1 =± (1+α ) α β ]
Restoration Matrix A- = A+ S ( s s S = 11 12 s 21 s 22 E. Thrane, LINAC22 q 1=± ) q 2 = q 3= 2 Ds11+s 12+2D s 21+2Ds22 2 2D s 12 s12 +2D s 22 2 D (1+q 1 s12 ) q1 q 2 D q 1 q 2 s 11 s 21 2 1+(2Dq 1 +Dq 2 ) s11+ D q 2 (q1 +s 21) After skew Q channel, ± n ϵ (ϵ ) +( γβ L) ±(γβ L) u 2 n ϵ+n n ϵ 2 (ϵun )2 (2 γβ L)2 eb σ 2c L= pz
P.Piot, Y.-E Sun, K.-J. Kim PRSTAB(9)311(26) Emittance Ratio 1 was achieved.
Possible Applications a) Emittance exchange is useful to optimize the phase-space distribution to applications. b)examples are a)pre-bunched FEL, b)coherent Smith-Parcels radiation, c)extremely short pulse generation, d)high aspect ratio beam for linear colliders
High Gain FEL Neil Thompson., et al. "The 4GLS VUV-FEL." University of Strathclyde (211).
Coherent Radiation with Bunch Train Y.-E Sun, et al., PRL(15)23481(21) v
Asymmetric Beam for Linear Collider a)linear Collider is an only solution for e+e- collision beyond the limit of ring colliders by the huge energy loss by synchrotron radiation. b)the beam is one pass and the beam current is very limited. In order of 1mA for linear colliders, and in order of A for a modern ring collider. c)to obtain an enough luminosity, the beam is focused down to nm.
High Aspect Ratio Beam in LC 2 Event Rate N =σ L f rep n b N L= 4 π σx σ y Luminosity 2 Beamstrahlung σσyy«σ «σxx (Asymmetric (AsymmetricBeam) Beam) Disruption Parameter Value Horizontal size 64 nm Vertical size 5.7 nm Bunch length 3 m m Vertical Disruption 19.4 RMS energy by BS 2.4% Horizontal emi. 1 mm.mrad Vertical emi..4 mm.mrad ΔE N E 2 E (σ x +σ 2y )σ z 2Nr e σz D x, y= γ σ x, y (σ x +σ y ) Aspect ratio 25 is made up with 3km DR 23
High Aspect Ratio Beam by EMIX The high aspect ratio beam is generated by a 3km DR (Damping Ring) in the current design (ILC TDR).. I the beam can be generated directly from the injector with EmiX technique, the design can be much simpler.
Flat Beam Generation for LC The f lat beam (ex=1um, ey=.4um) can be generated with RFTB and TLEX. The beam is generated in a large size to compensate the space charge nonlinearity. ex=ey=45 um. By RFTB, it can be ex=66um and ey=.3. The ex is too large for LC. It should be exchanged with ez by TLEX.
High Aspect Ratio Beam Generation with EmiX B field laser Injector Linac Skew Quadrupoles Polarized Beam GaAs/GaAsP Super-lattice Dogleg Dipole Mode RF cavity Dogleg To booster
STF RF Gun L-band (1.3 GHz) normal conducting RF gun developed for FLASH/XFEL at DESY. By switching current of the bucking coil, solenoid f ield can be made on the cathode surface. In the simulation, that was.1 Tesla. Cathode Position
RFTB Section The beam is generated in.1 Tesla selenoid f ield. The canonical angular momentum is converted in the free-space. The beam is accelerated and the correlation is restored by skew-q channel. B field laser Polarized Beam GaAs/GaAsP Super-lattice Accelerator Skew Quadrupoles
Phase-space in RFTB Before 1st Skew Before 2nd Skew Before 3rd Skew After 3rd Skew
TLEX Section ex and ez are exchanged by TLEX beam line. The large ex after RFTB is transferred to Z space after TLEX. ex after TLEX section is same as ez before TLEX line. Dogleg Dipole Mode RF cavity Dogleg To booster
Phase-space in TLEX Before 1st Dogleg After dipole RF After 1st Dogleg After 2nd Dogleg
Emittance Evolution (norm. in um) ez ex Position ex ey ez Cathode 1.5 1.5 8.5 RFTB 16.45 8.5 TLEX 8.5.45 16.4 8.4e+5 ILC design 1 ey
Parameters Parameter Value Unit Bsol.1 T Initial emittance 1.5 mm.mrad Bunch length 12 ps (full width) Beam size 1.6 mm (rms) Gamma after acc. 49 g1 -.53 T/m g2.926 T/m g3 2.58 T/m alpha η (dispersion).3 rad.355 m ξ(mom. compaction).16 m RF voltage 1.29 MV (at λ)
Flat Beam Generation at STF and WFA RFBT experiment will be carried at KEK-STF. TLEX experiment will be carried out at ANL WFA. The f lat beam compatible to LC will be demonstrated in STF by introducing the TLEX beam line as a future proposal. RF TB + EX L T on i t c se KEK-STF ANL-WFA
Summary Emittance exchange gives a freedom to optimize the emittance partitioning among degree of freedom. Applications : High gain FEL, coherent radiation, extremely short bunch generation, flat beam for LC, etc. ILC compatible beam can be made with these techniques. Pilot experiments will be carried out at KEK-STF and ANL-WFA. It can be a proposal for a future plan of STF.
Acknowledgement P. Piot (Northrn Illinois University) J. Power (ANL) H. Hayano, N. Yamamoto, Y. Seimiya (KEK) S. Kashiwagi (Tohoku University) K. Sakaue, M. Wahio (Waseda University)