To: e.mckigney@ic.ac.uk
Hi Ed:
Here is my NuFact02 talk for the WG1 session. It is in ASCII
and I have it on plastic. I hope you can accept this format.
Best Regards,
Don Summers
1) Muon Acceleration
with Fast Ramping Synchrotrons
D.~J.~Summers
University of MississippiOxford
NuFact02: Neutrino Factory Workshop 2002
Session WG1, Lecture Theater 2, 4 July 2002, 10:00 a.m.
Department of Physics, Blackett Laboratory
Imperial CollegeLondon, Prince Consort Road
London SW7 2BW, UK
16 July 2002
2) ACCELERATE WITH A RING FROM 2 to 20 GeV/c
Take a 1.7 Telsa field and a 70% packing fraction.
1) 95% iron lamination packing
2) field loss due to gradient dipoles
3) space for one kicker
4) 11 spaces for RF cavities
1.7 Tesla x 70% = 1.19 Tesla
For a ring with p = 20 GeV/c,
Radius = p/.3*B = 20/.3*1.19 = 56 meters
Circumference = 2*pi*R = 352 meters
A small ring.
3) 15 MV/m SUPERCONDUCTING RF CAVITIES
Scenario #1
1/2 GeV of 200 MHz cavities in 11 spaces
Accelerate from 2 to 20 GeV in 36 orbits
Highest decay losses during the first few orbits
77% of the muons survive, a bit low
Scenario #2
Add beam loading.
A 75cm long, 200 MHz cavity stores a kilojoule
(see J. Delayen et al. (JLAB), PAC2001, page 3380,
accelconf.web.cern.ch/AccelConf/p01/PAPERS/RPPH067.PDF)
To get 1/2 GeV, use 44 11.25 MeV cavities
44 kilojoules of stored energy
add 18 GeV to 10**13 muons
(18 x 10**9) (1.6 x 10**19 Joules/eV) (10**13) = 29 kJ
so 29/44 = 66% of the energy goes to the muons
The stored energy goes as E**2
So 0.33 of the Joules remain at 20 GeV/c
And SQRT(0.33) = 0.57 of the gradient or 8.5 MV/m remains
Accelerate from 2 to 20 GeV in 48 orbits
73% of the muons survive, a bit lower
Scenario #3
Add 1/2 GeV of less costly 400 MHz SCRF.
Lowers losses in early orbits,
while not increasing the end ramp rate at high B**2.
11 kilojoules of stored energy in the 400 MHz SCRF
Accelerate from 2 to 20 GeV in 30 orbits
Gains 1/3 GeV in orbit 30.
84% of the muons survive.
4) CHOICES FOR IRON LAMINATIONS
See D. Summers, http://arXiv.org/pdf/physics/0109002 and
H. Sasaki, KEK91261 for more details.
Material Composition rho B_Max Hc Thickness
(uOHM (Tesla) (Oer (microns)
cm) steds)
Grain Oriented 3Si 97Fe 47 2.0 .1 50 100 175
NKK Super ECore 6Si 94Fe 82 1.8 50 100
Metglas 2605SA1 2C 3Si 14B 81Fe 135 1.6 .03 30
Choose 100 micron thick grain oriented silicon steel because
it has the highest saturation, has a steep BH curve, and
I need to stamp laminations good to 10 microns.
Metglas laminations pose an R&D project.
Ramping at 1/3 GeV / orbit
Field increases 1,7% in last orbit, a time of 1.2 microSEC
58 microSEC for a quarter cycle or f = 4300 Hertz
Calculate the eddy current losses in the magnets.
Power = (Volume) (2pi f B thickness)**2 / (24 * rho)
= (300*.4*.4) (2pi 4300 1.2 10**4)**2 / (24 * 47 x 10**8)
= (48) (10.5) / (1.13 x 10**5)
= 45 Megawatts
But its only "on" for 15 half cycles per second!!!!!!!!!!!!!
Duty factor = (15) (30 orbits) (352 meters) / (3 x 10**8 m/s)
= 5.3 x 10**4
Power = (45 Megawatts) (5.3 x 10**4) = 24 Kilowatts <<<
Hysteresis losses are much less than the 15 Hz Fermilab Booster.
Eddy currents losses go as f**2, but hysteresis losses go as f**1.
Carbon steel is a lot lossier than grain oriented silicon steel.
Lamination shape is changed within a single magnet to
minimize end losses while still alternating gradients.
5) EFFECT OF SKIN DEPTH ON IRON LAMINATIONS
References:
Lorrain and Corson, 3rd edition, pages 537542.
K. L. Scott (Lucent Tech), "Variation of the Inductance
of Coils due to the Magnetic Shielding Effect of Eddy
Currents in the Cores," Proceedings of the Institute of
Radio Engineers, 18 (1930) 17501764.
First get the skin depth.
Take mu = 4000
mu0 = 4pi x 10**7
rho = 47 x 10**8
f = 4300
SKIN = SQRT(2 rho / [2pi f mu mu0])
= SQRT(2 47 x 10**8 / [2pi 4300 4000 4pi x 10**7]
= 83 microns
Now get the inductance kept; following Scott
R = THICK/SKIN
L/L0 = (SKIN/THICK)*((SINH(R) + SIN(R)) / (COSH(R) + COS(R)))
= 0.936
So one is off by 7% with 100 micron laminations
With 50 micron laminations, L/L0 = 0.996 or very little loss;
but they cost more per kilogram and packing fraction is lower.
100 microns may still be OK.
As saturation occurs, mu goes down, and the skin depth goes up.
And its only at the top end that complete penetration is needed.
6) TWO IRON REQUIREMENTS
A) B Field Must Follow Grain Orientation
B) Pole Faces Must Be Held Rigidly.
*******************
* * **
* * 2 * *
* **** **** *
* * * * * *
* * ******* * *
*1 * * 3*
* * ******* * *
* * * * * *
* **** **** *
* * 4 * *
* * **
*******************
Even Lamination (gradient not shown).
4 piece Grain Oriented
Silicon Steel Lamination
for an Hframe magnet.
Flux travels to the right.
The "C" on the left gives
mechanical support.
*******************
** * *
* * 2 * *
* **** **** *
* * * * * *
* * ******* * *
*3 * *1 *
* * ******* * *
* * * * * *
* **** **** *
* * 4 * *
** * *
*******************
Odd Lamination (gradient not shown).
4 piece Grain Oriented
Silicon Steel Lamination
for an Hframe magnet.
Flux travels to the left.
The backward "C" on the
right gives mechanical
support.
7) MAGNET POWER SUPPLIES  LC CIRCUITS
See D. Summers, http://arXiv.org/pdf/physics/0109002
Calculate the energy stored in an 0.06m high by 0.08m wide gap
of a 25 meter long magnet. Gradients are alternated by changing
pole shapes within magnets to minimize the number of ends.
Twelve magnets will be required.
W = [Volume] B**2 / (2 u0)
= [25 x ,06 x .1] 1.7**2 / (2 4pi x 10**7)
= 173,000 Joules
NI = B h / u0 = 1.7 .06 / 4pi x 10**7
= 81,000 Ampereturns
Let N=1
L = 2 W / I**2 = 5.3 x 10**5 Henries
C = 1/L(2pi f)**2 = 2.6 x 10**5 Farads
V = SQRT(2W/C) = 115,000 Volts
So the VA requirement is 115kV x 81kA,
which is met by 520 ABB Semiconductor
4500V 4000A GTO Thyristors costing $850 each.
For 12 magnets the parts cost is $5.3 Million.
173,000 / 520 = 340 Joules in the capacitor
attached to each thyristor.
C = 2 W / V**2 = (2 340) / 4500**2 = 33 uF
So buy two capacitors at $25 each from H & R
4500V 16uF GE 28F2009 4.5" x 2.81" x 10"
http://www.herbach.com $320K for capacitors
New capacitors will cost more.
8) CALCULATE LOSSES IN THE COPPER COILS
See H. Sasaki, KEK91261 for more details.
First calculate the skin depth in copper at 4300 Hz
to set a maximum wire size.
SKIN = SQRT(2 rho / [2pi f mu0])
= SQRT(2 1.7 x 10**8 / [2pi 4300 4pi x 10**7]
= 1.0 mm
So see how 30 gauge, width = 0.25mm copper wire does.
Supplier: http://www.mwswire.com/litzmain.htm
Take one turn of 0.05m square copper
The length is 50 meters.
R = 50 (1.8 x 10**8) / .05**2 = 360 uOHMS
P = I**2 R (INT cos**2) = 81000**2 360 x 10**6 .5
= 1.2 MegaWatts
Divide by 2000 for the duty cycle > P = 600 Watts
Next do the eddy current loss. Take an 0.1 Tesla fringe
field, which is half the reason to use iron!!!!
P = [Volume] (2pi f B w)**2 / (24 rho)
= [50 .05**2] (2pi 4300 0.1 .00025)**2 / (24 1.8 x 10**8)
= [0.125] (0.46) (2,300,000)
= 132,000 watts/magnet
So multiply by 12 for 12 magnets and
divide by the duty factor of 2000. P = 800 watts.
The two choices for water cooling tubes are either
316L stainless steel with a resistivity of 74 uOHMcm
or Titanium 6Al4V with a resistivity of 171 uOHMcm
In physics/0109002, even 316L loses less than the copper.
9) ACCELERATE WITH A RING FROM 20 to 180 GeV/c
Take a 1.7 Telsa field and a 70% packing fraction.
1) 98% iron lamination packing
2) field loss due to gradient dipoles
3) space for one kicker
4) 11 spaces for RF cavities
1.7 Tesla x 70% = 1.19 Tesla
For a ring with p = 180 GeV/c,
Radius = p/.3*B = 180/.3*1.19 = 504 meters
Circumference = 2*pi*R = 3167 meters
The same size as the Fermilab main injector.
Again accelerate in about 30 orbits.
10) ACCELERATE WITH A RING FROM 180 to 1600 GeV/c
See D. Summers, http://arXiv.org/pdf/physics/0109002
Use interleaved fixed 2 meter long 8 Tesla superconducting dipoles
and 3/6 meter long iron magnets ramping form 1.7 to +1.7 Tesla.
Short lengths give small sagittas.
3m 2m 6m 2m 3m
________________________________________________________________
V SC  +1.7T Grad8T SC  +1.7T Grad 8T SC +1.7T GradH SC
Quad  ient Dipole Dipole ient Dipole Dipoleient Dipole Quad

^

Gradient
changes
here
The gradient dipole magnetic field starts at 1.7 Telsa and ends at
+1.7 Tesla. At the start of an acceleration cycle, the gradient
dipoles oppose the bending and focusing of the superconducting
quadrapoles and dipoles. At the end of an acceleration cycle,
the gradient dipoles bend and focus in the unison with the
superconducting quadrapoles and dipoles.
Take a 3.5 Telsa field and a 70% packing fraction.
3.5T x 0.7 = 2.45 Tesla
For a ring with p = 1600 GeV/c,
Radius = p/.3*B = 1600/.3*2.45 = 2200 meters
Circumference = 2*pi*R = 13,800 meters
The same size as the the FNAL or BNL sites.
Accelerate in about 60 orbits. Note that doubling
the B field, halves the decay losses per orbit.
Now there is some time to refill an RF cavity
during the acceleration cycle.
The cost of 25 MV/m, 1300 MHz TESLA cavities is appealing,
if they can be made to work in this application.
11) SUMMARY
Scenarios to ramp from
2 to 20 GeV/c
20 to 180 GeV/c
180 to 1600 GeV/c
Low Duty Cycle, Fast Ramping Magnets
Seem to Warrant Further Study.
What is new?
1) Exploit the low duty cycle!!!!!!!!!!
2) Exploit Grain Oriented Silicon Steel.
High Saturation, Steep BH curve.
Use combination "C" / "H" laminations
to make rigid magnets.
3) Use thin laminations to minimize eddy currents.
4) Switch gradients inside dipoles to minimize ends.
5) Use thin copper wire to minimize eddy currents.
Sacrifice some I**2 R losses.
Don't worry too much about packing fraction.
6) Accelerate faster in the first few orbits
with cheaper, higher frequency superconducting
RF when the gamma boost is low.
7) Accelerate muons in opposite directions
in alternate cycles to save polarity
reversing switches in the 2 to 20 and
20 to 180 GeV/c rings.
8) See if low cost, 25 MV/m 1300 MHz TESLA SRF
can be used in the higher energy rings.
9) Interleaved fixed superconducting and fast
ramping magnets for the 180 to 1600 GeV/c ring.
Twice the energy for a given site size.