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Possibility of Luminosity upgrade of KEKB

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Possibility of Luminosity upgrade of KEKB Powered By Docstoc
					Beam-beam effect in super-B


            K. Ohmi
       MAC2007 for KEKB,
        19-21, Mar. 2007
Two approach toward high luminosity
• High current, high beam-beam parameter.




• Low emittance, low beta, low current, so-
  called super bunch collision

 x
         s
               Super B parameters
             SuperKEKB           Middle              SuperB (LNF/SLAC)
ex                  9.00E-09              6.00E-09            0.8E-09
ey                  4.50E-11              6.00E-11              2E-12
bx (mm)                    200                 50                   9
by (mm)                      3                 0.5               0.133
sz (mm)                      3                  6                   6
ns                       0.025                0.01         0.012/0.026
ne                  5.50E+10              5.50E+10            1.9E+10
np                  1.26E+11              1.27E+11            3.3E+10
q/2 (mrad)                   0                 15                  25
xx                       0.397               0.022
xy                0.794->0.24                0.179
Lum (W.S.)               8E+35            1.00E+36           1.00E+36
Lum (S.S.)          8.25E35 8-9E35
       Comparison of two approach
                         e xbx                                               e xbx
High curent                     1 or q  0     Low emittance                      1
                         qs z                                                qs z
                                                                    Overlap factor
            N2                                                       N2
 L                                                     L
        e x b xe y b y                                       1  q 2s z e y b y
               N                                                               bx
       xx                                            xx
                                                                 N
               ex                                                              ex
                                                              1  q 2s z
            by                                                   N             by
 xy   N                                               xy
        e x b xe y                                            1  q 2s z       ey
      by  s z                                               by 
                                                                     e xbx
                                                                      q
                  q: half crossing angle      xx is smaller due to cancellation of
                                              tune shift along bunch length
           High current approach
                                                 by
                              Keep e x , b x and    .
           N2                                    ey
L
       e x b xe y b y             e yby  0

      xx
              N                  L 
              ex
                               b y  s z limits luminosity
           by
xy   N                     • High current, Small coupling
       e x b xe y
                           • Choice of operating point
     by  s z
                        n x  0.5 x y                N 
                        q=0        L 
     Low emittance approach
              N2
 L                             by     bx       e xbx
       qs z e y b y     Keep      ,      and         .
                               ey     ex       by
         N         bx
xx                              e yby  0
       qs z        ex

                                L 
        N       by
xy
       qs z     ey

by 
        e xbx           • Bunch length is free.
         q
                        • Small beta and small
                          emittance are required.
      High current approach
• Reinforce RF system to store high current.
• Operation cost due to the high current.
• Heating of hardware, chamber, mask ....
• High beam-beam parameter with head-on
  collision: high nonlinear system.
• Sensitive for noise and error due to high
  beam-beam parameter.
• Limit of bunch length, instability and
  coherent synchrotron radiation.
      Low emittance approach
• Low emittance, magnet system should be
  reinforced.
• Low beta, the strongly focused IR, may be limit
  dynamic aperture.
• Single turn or multi turn injection. Multi-turn
  injection requires wide dynamic aperture, while
  single turn injection requires a high speed
  kicker (~2ns). A low emittance damping ring and
  high precision injection are required.
• High sensitivity due to the very low emittance.
• The main ring is similar to ILC damping ring
  equip with the final focus system of ILC.
• Crab crossing




                                           Crab cavity
• Crab waist
                                           Sextupole
                                           magnet



               Particles collide another
               beam at their waist point
     Super B with high current approach
             SuperKEKB           Middle              SuperB (LNF/SLAC)
ex                  9.00E-09              6.00E-09            0.8E-09
ey                  4.50E-11              6.00E-11              2E-12
bx (mm)                    200                 50                   9
by (mm)                      3                 0.5               0.133
sz (mm)                      3                  6                   6
ns                       0.025                0.01         0.012/0.026
ne                  5.50E+10              5.50E+10            1.9E+10
np                  1.26E+11              1.27E+11            3.3E+10
q/2 (mrad)                   0                 15                  25
xx                       0.397               0.022
xy                0.794->0.24                0.179
Lum (W.S.)               8E+35            1.00E+36           1.00E+36
Lum (S.S.)          8.25E35 8-9E35
Beam-beam Interaction and crossing angle
• Beam-beam interaction as a transformation of
  dynamical variable.
             X  exp   : (U3  U4  ...) : x0
• x4 , y4 term decrease but another coupling term
  increases for crossing angle. A kind of symmetry
  breaking degrade luminosity performance.
4-th order Coefficients due to crossing angle
• Coefficient of U4(x,y,z).
                 x4                       y4




               xpy2z           300010   x3z
                 Crab waist
• Add sextupole magnets at both side of
  collision point for finite crossing collsion.
• Effective potential is expressed as follows,
  U(x,y,z)d(s-s*)+Kxpy2d(s-s*-e)-Kxpy2d(s-s*+e)
Put sextupole magnets both side of the collision
  point at the vertical betatron phase difference,
  p(2n+1)/2 and horizontal mp.
4-th order Coefficients as a function of crab
            sextupole strength,




                    • H=K x py2/2, theoretical
                      optimum, K=1/xangle.
                    • Clear structure- 220,121
                    • Flat for sextupole
                      strength- 400, 301, 040
• Crab waist sextupoles cancel some coupling terms
  induced by crossing angle, while keep the synchro-
  betatron terms.
• H=25 x py2. Luminosity for crab waist is comparable with
  that of crab crossing for a parameter range.
                               Luminosities for crab crossing and
                               crab waist is not always same.
                           Equilibrium


                                                   ns=0.016
Tune scan, nx-ns
      • Efficient region of the Crab
        waist scheme is not wide.
      • Low ns.
      • High nx degrades the
        performance independent
        of crab waist. Synchro-
        beta dominant.
 Horizontal tune half integer nx=0.5
• Particles interact with fixed beam at x and –x mutually.
  The phase space structure in y-py at x is the same as
  that at -x, because of symmetry of the fixed beam.
• System is one dimension, beam-beam tune shift is 0.5
• KEKB tries to realize a high luminosity with this
  technique.
• A high precision tuning is required.

                                          y




                                                        x
For crab waist at low emittance
• Synchro-beta transformation term as x3z,
  which is induced by crossing angle and is
  not cancelled by the crab sextupole,
  disturbs luminosity performance near the
  half integer tune.
• In KEKB low emittance operation, a beam-
  beam instability has been observed.
• Operation strategy is completely different
  from the present one.
          Super B with meddle parameter
             SuperKEKB           Middle              SuperB (LNF/SLAC)
ex                  9.00E-09              6.00E-09            0.8E-09
ey                  4.50E-11              6.00E-11              2E-12
bx (mm)                    200                 50                   9
by (mm)                      3                 0.5               0.133
sz (mm)                      3                  6                   6
ns                       0.025                0.01         0.012/0.026
ne                  5.50E+10              5.50E+10            1.9E+10
np                  1.26E+11              1.27E+11            3.3E+10
q/2 (mrad)                   0                 15                  25
xx                       0.397               0.022
xy                0.794->0.24                0.179
Lum (W.S.)               8E+35            1.00E+36           1.00E+36
Lum (S.S.)          8.25E35 8-9E35
     Strong strong simulation results for the
        middle case, high current & low b
                                                            • Crab waist option of
     L
                                                              Super KEKB,
                                                              longitudinal slice,
8    10 35                                                    Nslice=20, 1000 turn.
6    1035
 4
 2
      1035
      1035
                                                        8
                                                            • Scan area
                                                    6
           0
                                                            • 0.503<nx<0.603
               2                                  4 nuy
 (0.5,0.53)        4
                         6                                  • 0.53<ny<0.6
                   nux                       2
                                 8
                                      10                    • 0.01 step
                                     (0.6,0.53)

         sx                                                     sy

0.00006                                                      1.5 10   6
0.00005                                                 8
0.00004                                                        1 10   6                                      8
 0.00003                                            6                     7
 0.00002                                                       5 10                                      6

               2                                  4 nuy               2                               4 nuy
(0.5,0.53)         4                                          (0.5,0.53)      4
                             6                                                      6
                       nux       8           2                                nux       8         2
                                       10                                                   10
                                     (0.6,0.53)                                             (0.6,0.53)
        Near integer tune: high current & low b
                                                       •     0.033<nx<0.103
    L
                                                       •     0.03<ny<0.1
1.75
 1.5
1.25
        10 35
        1035
         1035
                                                8      •     0.01 step
         10 35
                                                       •
    1                                       6

                 2                       4 nuy
                                                             Lum. is better at
 (0.03,0.03)           4
                     nux   6         2
                                                             higher tunes in both,
                                 8
                               (0.1,0.03)
                                                             but still low.

        sx                                                      sy


0.00006                                                       1.6 10 6
                                                8(0.1,0.1)    1.4 10 6                              8
0.00005
 0.00004                                    6                  1.2 10 6                         6

         2                               4 nuy                (0.03,0.03)
                                                                        2                     4 nuy
 (0.03,0.03)                                                                  4
                       4
                     nux             2                                      nux   6       2
                           6
                                 8                                                    8
                               (0.1,0.03)                                             (0.1,0.03)
       Weak strong simulation results for the
        middle case, high current & low b
       L                                                                                     •    Crab waist option of
                                                                                                  SuperKEKB
                                                30                                           •    0.503<nx<0.803
  1    10 36                                    25
                                                                                             •    0.503<ny<0.803
7.5    1035                                30                                                •    0.01 step
   5    1035
2.5     10 35                                   20

            0                           20

(0.5,0.8)
           30
                                   10
                                         nux    15
                                                                                             •    Stopband is narrower
                20
                                                10
                                                                                                  in the weak-strong
                 nuy   10
                                                                                                  simulation. Note that
                            (0.5,0.5)            5
                                                                                                  the horizontal size of
                                                     5        10   15    20        25   30
                                                                                                  one beam is fixed.
           sx                                                           sy



  0.0001                                                 4    10 6
0.000075                                  30             3    10 6                                                 (0.8,0.5)
                                                                                                                  30
 0.00005                                                 2     10 6
0.000025                                                  1    10 6
         0                              20                                                                   20
                                                                   0
       30                                nux                     30                                          nux
(0.5,0.8)       20                10                     (0.5,0.8)            20                        10
                nuy    10
                                                                              nuy       10
                            (0.5,0.5)                                                            (0.5,0.5)
             Super B with low e and low b
               SuperKEKB           Middle              SuperB (LNF/SLAC)
ex                    9.00E-09              6.00E-09            0.8E-09
ey                    4.50E-11              6.00E-11              2E-12
bx (mm)                      200                 50                   9
by (mm)                        3                 0.5               0.133
sz (mm)                        3                  6                   6
ns                         0.025                0.01         0.012/0.026
ne                    5.50E+10              5.50E+10            1.9E+10
np                    1.26E+11              1.27E+11            3.3E+10
q/2 (mrad)                     0                 15                  25
xx                         0.397               0.022
xy                  0.794->0.24                0.179
Lum (W.S.)                 8E+35            1.00E+36           1.00E+36
Lum (S.S.)            8.25E35 8-9E35
           Weak-strong simulation for low e and low b
                         (LNF/SLAC)
    • Longitudinal slice, Nslice=200
    • 0.503<nx<0.803, 0.503<ny<0.803, 0.01 step

                       L                                  sx                                      sy


1 10 36                                                                                7
                                     30 0.00004                                30 1 10                                  30
     35
5 10                                    0.00002                                   5 10 8
       0                          20           0                            20          0                          20
                                   nuy  (0.5,0.5) 10                         nuy(0.5,0.5) 10                       nuy
(0.5,0.5) 10                 10                                        10                                     10
       0.6 nux    20                            0.6 nux    20
                                                                                       0.6 nux   20
                        30                                       30                                      30
                 nx, ny=(0.8,0.5)                               (0.8,0.5)                             (0.8,0.5)
• 0. 03<nx<0.303, 0.03<ny<0.303, 0.01 step
• Wide region with horizontal blow-up near nx~0. Similar
  as strong-strong.

                L                                sx                                     sy


  1    10 36                                                                                     2    10 6
                                                    0.00004                                 30 1.5    10 6                                  30
7.5    1035                                      30 0.00002                                      1    10 6
   5    1035                                                                                      5    10 7
2.5     10 35                                              0                           20                 0                            20
            0                                 20
           30                                                                          nuy                                             nuy
                                               nux                                                    (0,0.)   10                 10
                                         10           (0,0.)   10                 10
 (0.3,0.)           20
                                                                nux   20                                        nux   20
                     nuy   10
                                                                            30                                               30

                                (0,0.)                                 (0.3,0.)                                            (0.3,0.)

       Strong-strong simulation for the low e and low b
       design is difficult, because a bunch should be sliced
       too much pieces in the longitudinal.
       Stopband width in the strong-strong simulation may
       be the interesting issue for the collision scheme.
                     Summary
• The crab crossing is being studied in KEKB now.
• We understand how accurate tuning we can and have to
  do in KEKB.
• The crab waist scheme will be studied in DAFNE and
  KEKB in the near future.
• Synchro-betatron stop-band in the crab waist scheme,
  which is remarkable in the strong-strong simulation, is
  important issue. The low tune shift may help the
  stopband width.
• It is difficult to simulate the low e and low b parameter
  with the strong-strong method now.
• We have to have a solution of dynamic aperture and
  injection scheme in the low emittance scheme.
• It becomes clear how and which way we choose
  gradually (soon).

				
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posted:9/5/2011
language:English
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