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Exchange of Transverse and Longitudinal Emittance at the A0

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					 Exchange of Transverse and
Longitudinal Emittance at the
      A0 Photoinjector

                Tim Koeth
(this talk was initially prepared for TK’s
committee meeting of March 11, 2008)
       Updated March 14th, 2008
                    Outline
•   Brief Photoinjector introduction
•   Motivation & Theory of Emittance Exchange
•   Exchange Apparatus at the A0 Photoinjector
•   Results to date…
•   Next Steps
•   Acknowledgements
                    The A0 Photoinjector
Next, Artur will talk about the low level
RF systems that keep the laser, two 1.3
GHz and one 3.9 GHz systems in sync.




                                 •   Laser energy 16 mJ/pulse @ 263nm
                                 •   <5nC/bunch (have had >12 nC in the past)
                                 •   Typically 10 bunches/RF pulse. 1 Hz rep rate
                                 •   4 MeV gun output energy
                                 •   16 MeV total energy
                                 •   Dp/p ≈ 0.3%@ 16MeV (1nC)
                                 •   Bunch length ≈ 2 mm (1nC)
                                 •   gez ≈ 120 mm-mrad (RMS @ 1nC)
                                 •   gex,gey≈4 mm-mrad (RMS @ 1nC)
    The Idea: Emittance Exchange (EEX)
•   In 2002 M. Cornacchia and P. Emma proposed using a TM110 deflecting
    mode cavity in the center of a chicane to exchange a smaller longitudinal
    emittance with a larger transverse emittance for a FEL.
•   Kim & Sessler in 2005 proposed using a flat beam (ex<<ey) combined with a
    deflecting mode cavity between 2 doglegs to produce a beam with very
    small transverse emittances and large longitudinal emittance to drive an
    FEL.
•   We are doing a proof of principle emittance exchange at A0 using the
    double dogleg approach with a round beam (ex=ey) .
     – We’ll be exchanging a larger longitudinal emittance with a smaller transverse
       emittance.
     – Keep in mind that emittance is the area beam phase space, e  x 2 x'2  xx' 2
•   Why ?
     • Basic and unique beam dynamics manipulation – proof of principle
     • FEL’s - low transverse emittance, large brightness
     • This phase space manipulation could have application in a linear
       collider
         TM110 (Deflecting) Mode Cavity
                           a




                                      (from Figure 1 of C&E)
                               Electric field at synchronous phase.
                               Magnetic field a quarter period later.


                                                                          k
•   No longitudinal electric field on axis.                                       eV0
•   Electric field imparts an energy kick
    proportional to distance off axis.
     –   Plan to use this to change the
                                                  kx                            aE

                                                x'  kz
         momentum deviation in presence of
         dispersion!                                                    k is the integrated
•   Electro-magnetic field provides                                     longitudinal energy gain
    deflection as a function of arrival time.                           at a reference offset a
•   This is the type of cavity used as a crab
    cavity or for bunch length                                          normalized to the beam
    measurement.                                                        energy E.
       Concept of Emittance Exchange
A typical non-dispersive transport matrix:

                      x    A11       A12     0      0  x 
                                                        
                      x'   A21       A22     0      0  x' 
                      z  0              0   D11   D12  z 
                                                        
                          0                       D22   in
                      out                0   D21        
What we want to develop is a matrix like:


                      x     0   0            B11   B12  x 
                                                        
                      x'    0   0            B21   B22  x' 
                      z   C   C12            0     0  z 
                            11                          
                          C                        0   in
                      out  21 C22             0         
                             EEX: Linear Optics Model
 Initial e- bunch    D1                          3.9 GHz TM110


                                   D2                              D3


                                                                                   final e- bunch
                                                                         D4




First, break the EEX-line into three sections:                                    ex > ez
           Magnetic dogleg before cavity: Mbc
           TM110 cavity (thin lens): Mcav
           Magnetic dogleg after cavity: Mac
                                    1 L 0 D                                     1      0 0 0
                                                                                            
                                     0 1 0 0                                    0      1 k 0
                    M bc  M ac                                  and   M cav   
                                      0 D 1 D                                     0     0 1 0
                                                                                            
                                    0 0 0 1                                     k
                                              
                                                                                         0 0 1
                                                                                               
                                                  1 L 0 D  1    0 0 0  1 L 0 D 
                                                                                
   To get:                                        0 1 0 0  0    1 k 0  0 1 0 0 
                          R  M ac M cav M bc   
                                                   0 D 1 D  0   0 1 0  0 D 1 D 
                                                                                
                                                  0 0 0 1  k    0 0 1  0 0 0 1 
                                                                                
                      EEX: Linear Optics Model
                      1  Dk L  Dk  (1  Dk ) L  kL    D  D(1  Dk )  DkL 
                                                                                   
                       0          1  Dk            k            Dk               
                    R
                        Dk D  D(1  Dk )  aDkL 1  Dk D  D 2 k  ad (1  Dk ) 
                                                                                   
                       k                                        1  Dk             
                                     kL             0                              

Now if we take the trivial case of k =0 we get:
                                    1 2L           0  2D 
                                                         
                                   0 1             0   0 
                                 R
                                     0 2D           1 2D 
                                                         
                                   0 0                 1 
                                                   0     

However, if we take the special case of k = -1/D = ko we get:
                                                       L         
                                  0         0             D  L 
                                                       D         
                                                       1
                               R 0         0               
                                                        D         
                                        D  aL       0    0 
                                  1        L                    
                                                       0    0 
                                  D         D                    
All of the X-X and Z-Z coupling elements are zero !
                                  EEX: Linear Optics Model
                                                                 L         
                                          0                 0       D  L 
With our k=ko                                                    D         
                                                                 1
                                       R 0                 0            A B 
                                                                  D          
                                                                                  
                                                                                   
                                                 D  aL        0    0     C D
                                          1         L                     
                                                                 0    0 
                                          D          D                     
We can transports the initial uncoupled beam (sigma) matrix through the EEX line
                          e x0  x    e x0  x     0               0      
                                                                           
                                                                                                  And remember det x   e x
                 0    e x0  x    ex g x        0               0                                                      2
        o   x                        0
             0
                  z   0
                                        0        e z z
                                                     0
                                                                  e z0  z 
                                                                            
                          0              0        ez z         e z0 g z 
                                                        0                  

  via        R o RT :
                                 A xo AT  B zo BT                           A xo C T  B zo DT 
                              
                                 C x AT  D z BT
                                                                                                     
                                                                                                   T 
                                     o          o
                                                                                C xo C  D zo D 
                                                                                       T



 We know from above that A = D = 0, so this reduced to:
                                           B zo B T                           0  
                                        
                                          
                                                                                   
                                                                                 T 
                                              0                          C xo C 

 Then take the determinate of σx, σz and we get:                                    det x   e z2   det z   e x
                                                                                                                     2



   a complete swap of the emittances is seen.                                        ex  ez
       EEX Beam Line at the Photoinjector
                                                                                        Vertical bend
                                                                                        avoids residual
                                                                                        dispersion of X-
                                                                                        plane




               Diagnostics:




     = Beam Position Monitor (BPM)             = Diagnostic cross: viewing screen(s) & digital camera
     - Transverse beam position                - Measuring transverse beam size
                = Slit/Screen pair for transverse emittances.       = MagneticSpectrometer – P & ∆P
Not shown: Streak camera & Interferometer – e- bunch length, Phase Mon – e- TOF
EEX Beam Line at the Photoinjector
Vertical
Spectrometer         Dipoles




 TM110 Cavity

                               Beam
                               direction
   EEX Beam Line at the Photoinjector (Cav off)
               25
                        Beamline Layout                          1.2
                                                                 1
               20               betax                            0.8
                                betay                            0.6
                                etax
               15                                                0.4
    beta (m)




                                                                        eta (m)
                                etay
                                                                 0.2
               10                                                0
                                                                 -0.2
                5                                                -0.4
                                                                 -0.6
                0                                                -0.8
                    5   6   7    8            9   10   11   12
                                       s(m)


Deflecting Mode Cavity
TM110 Cavity Details
         Construction:
          5 cells (of CKM design)
          Punched OFHC Copper
          Vacuum brazed
         Radio Frequency:
          3.9 GHz (3x 1.3GHz)
          Q300K=14,900
          Q80K=35,600
          Coupling (β) = 0.7
          Req’d RF power @ full gradient: 50kW
            Cavity Polarizaton and Field Flatness
  Red: theory                                        0
Black: fit cell 2                              355         5
                                     345 350                   10 15
 Blue: fit cell 3              340                                         20
                            335                                                 25
Green: fit cell 4        330                                                         30
                      325                                                                 35
                   320                                                                         40
                 315                                                                                45
               310                                                                                       50
             305                                                                                           55
           300                                                                                               60
          295                                                                                                 65
      290                                                                                                         70
                                                                                                                             6

     285                                                                                                           75
    280    Vertical                                                                                                80
                                                                                                                             4
    275                                                                                                                85
    270                                                                                                                90
    265                                                                                                                95
                                                                                                                             2
    260                                                                                                            100
     255                                                                                                           105
      250                                                                                                         110
                                                                                                                             0
          245                                                                                                 115
                                                                                                                                  0       50      100   150   200   250   300   350   400   450
           240                                                                                 120
             235                                                                             125
               230                                                                         130                               -2
                 225                                                                     135
                   220                                                                 140
                      215                                                           145
                         210                                                     150
                            205                                               155                                            -4
                               200                                         160
                                     195 190                         165
                                               185         175 170
                                                     180

                                                                                                                             -6


•         Longitudinal electric field vs angle in                                                                            -8

          cells 2-4 determined by bead pull.
                                                                                                                            -10
•         Cavity polarization is set by input
          coupler                                                                                                                     •        Bead pull results of cavity field
                                                                                                                                               flatness tuning.
       TM110 Cavity: 1st Deflection


                                                                                    Operating phase
                                                                                     for exchange




   The induced kick is about 70% of what was expected for the input power, however, sufficient
    contingency was built into the cavity to accommodate this.
                                                 BPM26
Early Vertical Spectrometer Images

• Preliminary investigations showed
  encouraging results. For instance, as
  we increased the TM110 cavity                       ~ 550keV
  strength we saw a reduction in
  momentum spread…




              Spectrometer Screen
                                    Cavity 100%
                                     Cavity 70%
                                      Cavity80%
                                       Cavity40%
                                        Cavity: OFF
                                             50%
                                             60%
                                              10%
                                              20%
                                              30%
            Measuring the EEX Line Matrix
 There is exciting evidence that the cavity was indeed modifying the momentum
    spread, so we have begun to systematically measure the EEX beam line matrix.
Again, describing the beam line with linear optics we have:
                  x      R11     R12    R13    R14   R15   R16  x 
                                                                
                   x'    R21     R22    R23    R24   R25   R26  x' 
                   y    R        R32    R33    R34   R35   R36  y 
                      31                                       
                   y'    R41     R42    R43    R44   R45   R46  y ' 
                  z     R        R52    R53    R54   R55   R56  z 
                         51                                     
                                                          R66   in
                    out  R61     R62    R63    R64   R65        
Adjusting one input parameter at a time and measuring all output parameters we can
map out the transport matrix. For example, introducing a momentum offset yields
the 6th column:
                    Dx     R11    R12    R13   R14   R15   R16  0 
                                                                
                    Dx'    R21    R22   R23    R24   R25   R26  0 
                    Dy    R       R32   R33    R34   R35   R36  0 
                       31                                      
                    Dy '   R41    R42   R43    R44   R45   R46  0 
                    Dz    R       R52   R53    R54   R55   R56  0 
                           51                                   
                    D                                     R66  D in
                     out  R61     R62   R63    R64   R65        

Do this with the TM110 cavity off, partially on, 100% on, and greater
     EEX Beamline: Vertical Spectrometer BPM
  For a given TM110 strength, k, changed beam central momentum by ± 2.15 % in
  0.70% increments by varying 9-Cell cavity gradient. Repeated for several TM110 k:


                                                                                        TM110 cavity
                                                                                        strength, ko
                                                                                         90%
                                                                                         73%
                                                                                         OFF
                                                                                          105%
                                                                                         100%




Intro p from 9-Cell   Vary k
                                                                  Dx     R11   R12    R13   R14   R15   R16  0 
                                                                                                             
                                                                  Dx'    R21   R22    R23   R24   R25   R26  0 
                                   record vertical BPM reading            R
                                                                  Dy            R32    R33   R34   R35   R36  0 
                                                                     31                                     
                                                                  Dy '   R41   R42    R43   R44   R45   R46  0 
                                                                  Dz    R      R52    R53   R54   R55   R56  0 
                                                                         51                                  
                                                                  D                                    R66  D in
                                                                   out  R61    R62    R63   R64   R65        
EEX: Beam Line Horizontal Dispersion
 measurement with TM11O cavity off
                                               Lines: ideal
                                               Dots : Horizontal
              D1 D2   TM110   D3 D4   SPECT.
                                               BPM measured
                                               difference data

                                               δP = ± 1.05 %
                                               in 0.35 % increments



     +1.05%
     +0.70%
     +0.35%
     0
     -0.35%
     -0.70%
     -1.05%
EEX: Beam Line with TM110 Cavity On,
               Ideal:         Lines: ideal

                 D1 D2 TM110 D3 D4   SPECT.


                                              100%
                                               80%
                                                60%
                                              120%20%
                                                  OFF
                                                 40%




                                               δP = ± 1.05 %
                                               in 0.35 %
                                               increments


    +1.05%
    +0.70%
    +0.35%
    0
    -0.35%
    -0.70%
    -1.05%
EEX: Beam Line with TM110 Cavity on
            Measured:
                                           Cavity
              D1 D2 TM110 D3 D4   SPECT.
                                           strength, ko


                                            100%
                                           44%
                                            85%
                                            67%
                                           OFF




  +1.05%
  +0.70%
  +0.35%
  0
  -0.35%
  -0.70%
  -1.05%
     Streak Camera TOF measurements
Introduce p from 9-Cell




                                                                                                                                  Streak camera ~
                                                                                                                                  1pSec resolution




                    6
                                                                     y = 18.214x - 260.38
                    5                                                     R² = 0.9968               Dx     R11   R12   R13   R14   R15   R16  0 
                                                                                                                                              
                                                                                                    Dx'    R21   R22   R23   R24   R25   R26  0 
                    4               TM110 k=75%ko                                                   Dy    R      R32   R33   R34   R35   R36  0 
                                                                                                       31                                    
                                                                                                    Dy '   R41   R42   R43   R44   R45   R46  0 
     delta-z [mm]




                    3               TM110 off                                                       Dz    R      R52   R53   R54   R55   R56  0 
                                                                                                           51                                 
                                                                                                    D                                   R66  D in
                                                            y = 8.0444x - 115.04                     out  R61    R62   R63   R64   R65        
                    2                                               R² = 1


                    1

                    0
                     14.25   14.3      14.35        14.4   14.45      14.5         14.55    14.6
                    -1
                                                Beam energy [MeV]
Similar for 2nd Column: vary ∆xin’
    Impart Dx’ by adjusting a
    horizontal corrector
    magnet




                                 Dx     R11   R12   R13   R14   R15   R16  0      k=62%ko
                                                                           
                                 Dx'    R21   R22   R23   R24   R25   R26  Dx' 
                                 Dy    R      R32   R33   R34   R35   R36  0 
                                    31                                    
                                 Dy '   R41   R42   R43   R44   R45   R46  0 
                                 Dz    R      R52   R53   R54   R55   R56  0 
                                        51                                 
                                 D                                   R66  0 in
                                  out  R61    R62   R63   R64   R65        

 … And Dx, Dy, Dy’… The Dz can be achieved by adjusting the TM110 cavity phase
Dx’in data from today
Today’s BPM8/30 Dispersion Measurements




                    BPM8 & 30 Special 4-inch housing

                    Ray’s cald XS4 Vert Disp : 865mm
                    Tim’s measuremnt 855+/-5mm

                    Ray’s calc of XS3 Horz Disp: 225mm
                    Tim’s measurement 226mm

                    Finally nice agreement !
                    Note non-lin > 8 mm
     Summary of Today & yesterday
    data collection (March 13 thru 14)
        TM110 5-Cell off   25% ko       50% ko            75% ko             ~90% ko
∆x              X              X               X                 X                 X
∆x’             X              X               X                 X                 X
∆y              X              X               X                 X                 X
∆y’             X              X               X                 X                 X
∆z(ф)           -              X               X                 X                 X
δ               X              X               X                 X                 X
δ energy incriments calibration against BPM8

Now, off to analyze…                x      R11   R12    R13   R14   R15    R16  x 
                                                                                
                                     x'    R21   R22   R23    R24   R25    R26  x' 
                                     y    R      R32   R33    R34   R35    R36  y 
                                        31                                     
                                     y'    R41   R42   R43    R44   R45    R46  y ' 
                                    z     R      R52   R53    R54   R55    R56  z 
                                           51                                   
                                                                          R66   in
                                      out  R61   R62   R63    R64   R65         
            EEX: Next Steps
• Continue to populate the matrix
• Measure input and output emittances
• Graduate !
                        Many thanks go to:
•   Helen Edwards - Advisor
•   Don Edwards - Voice of reason
•   Leo Bellantoni – [tor]Mentor & CKM
•   Ray Fliller – A0 Post Doc
•   Jinhao Ruan – Laser, All things optical
•   Jamie Santucci – fireman
•   Alex Lumpkin – streak camera
•   Uros Mavric – Ph.D. Student
•   Artur Paytan – Yerevan U. Ph.D. Student
•   Mike Davidsaver – UIUC staff, controls guru
•   Grigory Kazakevich – Guest Scientist, OTRI
•   Manfred Wendt & Co – Instrumentation, BPMs
•   Elvin Harms – kindly sharing a klystron
•   Randy Thurman-Keup – Instrumentation, Interferometer
•   Vic Scarpine – Instrumentation, OTR and cameras
•   Ron Rechenmacher – CD, controls
•   Lucciano Piccoli – CD, controls
•   Brian Chase, Julien Branlard, & Co – Low Level RF
•   Gustavo Cancelo – CD, Low Level RF
•   Wade Muranyi & Co – Mechanical Support
•   Bruce Popper – drafter & artist
•   Chris Olsen - assistant

				
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posted:3/24/2012
language:English
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