Muons, Inc.

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Pulsed Magnet Arc Designs for Recirculating Linac
Muon Accelerators K.B.Beard1, R.P.Johnson1,
G.M.Wang1, S.A.Bogacz2 1Muons,Inc., 2Jefferson
Lab
current address BNL
LEMC2009 workshop 8-12 Jun 2009
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Getting ms from 3 GeV to 2 TeV before they all
decay away
The very big picture. dtm dtL/g (time
dilation) Dtm ?1/g dtL ? ?mo/(Eig x) dx/c
mo/gc ln(Ef/Ei) N/No e -l Dtm (Ef/Ei) -l
mo/gc
(average gradient over whole path)
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How to get m/- from 3 GeV to 2 TeV before they
all decay away?
m

• TELSA cavities
• real estate g 31 MeV/m
• 64.4 km linac
• 97 survival
• 40,000M

_at_Jlab 20M/GeV
g
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Reuse RF lots of schemes
Rapid Cycling Synchnotron
racetrack recirculating linac
dogbone Recirculating Linear Accelerator
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• from 3 to 31 GeV
• lower frequency, less gradient

500m 400MHz 8MV/m linac
DEpass 500m 8MV/m 4 GeV/pass Npass
(Ef-Ei)/DEpass 7
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• Thinking about it
• constant value linac quadrupoles provide
  progressively weaker focussing
• many arcs make for a complicated problematic
  switchyard

• What can we do about it?
• Use quadrupoles with constant but non-uniform
  settings that increase with distance to center,
  creating beta function beating A.Bogacz
• Use a Fixed Field Alternating Gradient
  (FFAG)-like arcs with very large (2.71)
  momentum acceptance G.M.Wang

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A.Bogaczs Bisected linac optics
Bisected linac Optics mirror symmetric
quadrupole gradient profile minimizing
under-focus beta beating
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G.M.Wangs FFAG arcs - Pmax/Pmin2.7 Po5.7 GeV
Bavg 0.7 T 0.2 Bmax
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3 to 31 GeV
small single pass superconducting arcs
m-
m
500m 400MHz 8MV/m linac
dual pass teardropsuperconducting FFAG arcs
Up to here, you can get away with dipoles and
quadrupoles that dont ramp in time but from
here on up its hard to avoid.
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The good news D.Summers et al has already
thought about it in detail for use in an RCS
lets just follow in his footsteps. Again,
stepping back for the big picture and discarding
details for now
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Arc Magnets

• superconducting magnets can have get up to
  8.8T, but can only ramp very slowly (seconds ?
  all ms decay)
• normal magnets can ramp quickly, but only up to
  1.8T (big arcs ? long paths, many ms decay)
• How about a hybrid, with normal magnets swinging
  from -1.8 to 1.8T and the superconducting
  magnets constant?

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Hybrid magnets
1.8T
1.8T
8.8T
Ln/2
Ln/2
Ls
Pmax/Pmin Bmax/Bmin (BsLs BnLn)
(BsLs - BnLn)
x (Pmax/Pmin-1)/(Pmax/Pmin1) Bavg f
(x1)/(x/Bn1/Bs)
BavgT
Pmax/Pmin?8, Bavg? 3.0T
Pmax/Pmin
Pmax/Pmin?8, Bs?8 Bavg?2 Bn
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30-2000 GeV concept
Pmax2 TeV, Bavg3T ? Rarc2.2 km Larc16.3
km Bavg1.8T ? Rarc3.7km
Larc27.4 km
? 90 m survival, DtLAB1 mS
? 84 m survival, DtLAB1.7 mS
4km 1.3GHz 30.8 MV/m linac, DE123.2 GeV
m
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Consider the dipoles can it be done? About the
same as D.Summers RCS
Very rough numbers (normal 1.8T magnets)!

• LEMC emittance (153 GeV, b20 m)
• s-N 2.1 mm-mrad ? 10 s-1.7 mm
• small aperture ? little stored energy 3.7 J/m
• power 2.2 kW/m (60 MW/arc)
• core losses 130 W/m
• resistive heating 800 W/m

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D.Summers, et al
LHC magnet
cartoon of LEMC magnet
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Don Summers talk this afternoon
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Also need pulsed quadrupoles in linac arcs
Some linac quads see a lower energy than the
any of the arc dipoles, so require a larger
aperture

• aperture (30 GeV, b20 m) 3 mm
• gradient (2 TeV, b20 m) 200 T/m
• W G2 r4/(8mo) ? 0.3 J/m ? 200 W ramp power

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Simplist quadrupole
G 200 T/m r 3 mm
3 mm
G dBy/dx 2 moI / pr2
2.3 kA W G2 r4/(8mo) ½ L I2 ½
(mo/p2) I2 ? L mo/p2 0.1 uH Vramp - L dI/dt
(DG/Dt) r2/(2p) 0.2 V
core losses 80 W/m
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Also need pulsed quadrupoles - What has been done?
FNAL combination booster magnets 6x
energy/length, switch in 1 mS
HCX fusion experiment pulsed quadrupoles about
840x energy/length (at a very low duty cycle)
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A few thoughts on scaling

• for dipoles, the stored energy power cost
• ? s-2 B2

• for quadrupoles, stored energy power cost
• ? s-4 G2

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30-2000 GeV
R3.7km normal magnets
FNAL site
R2.2km hybrid magnets 91 survival
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new idea Bloom - non-ramped small arcs
3-270 GeV
quad G ramped by time position
superconducting arcs
fast switches
m
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Conclusion

• average gradient over whole path determines m
  survivability
• ramped dipole magnets mean large arcs
• low emittance makes for small apertures ?
• little stored
  energy, power, costs
• most schemes require fast pulsed magnets of some
  kind
• Our thanks to D.Summer and colleagues

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Muons, Inc.