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traditionally ramping synchrotrons have provided economical particle acceleration . here
we explore a very fast ramping muon synchrotron for a neutrino factory @xcite .
the accelerated muons would be stored in a racetrack to produce neutrino beams as they decay ( @xmath0 or @xmath1 ) .
neutrino oscillations @xcite have been observed at experiments such as homestake @xcite , super 
kamiokande @xcite , and sno @xcite
. further exploration using a neutrino factory could reveal effects such as cp violation in the lepton sector which could explain the matter  antimatter asymmetry of the universe .
this synchrotron must accelerate muons from 4 to 20 gev / c with moderate decay loss . because synchrotron radiation goes as @xmath2 , muons radiate two billion times ( @xmath3 ) less power than electrons for any given ring diameter and lepton energy .
magnet eddy current losses are minimized by the low duty cycle of the machine plus thin iron laminations and copper conductors .
grain oriented silicon steel is used to provide a high magnetic field with a high @xmath4 to minimize magnetic energy stored in the return yoke . the magnetic energy stored in the gap
is minimized by reducing its size .
cool muons @xcite with low beam emittance allow this . stored energy goes as @xmath5 .
the voltage required to drive a magnet is equal to @xmath6 .
very high voltage is expensive .
@xmath7 must be large because of the 2 @xmath4sec muon lifetime , so the main option for lowering voltage is to shrink the volume of stored energy to reduce the inductance , @xmath8 .
acceleration to 4 gev might feature fixed field dogbone arcs @xcite to minimize muon decay loss .
fast ramping synchrotrons @xcite might also accelerate muons to higher energies for a @xmath9 collider @xcite .
as a first step , we form arcs with sequences of combined function cells formed within continuous long magnets , whose poles are alternately shaped to give focusing gradients of each sign .
an example of such a cell has been simulated using synch @xcite .
the example has gradients that alternate from positive 20 t / m gradient ( 2.24 m long ) , to zero gradient ( .4 m long ) to negative 20 t / m gradient ( 2.24 m ) to zero gradient ( 0.4 m ) , etc .
the relatively short zero gradient section is included to approximate a real smooth change in the gradients .
details are given in table 1 .
.combined function magnet cell parameters .
five cells make up an arc and 18 arcs form the ring . [
cols="<,^,^ " , ]     find the skin depth of copper at 4600 hz to see if .25 mm ( 30 gauge ) wire is useable .
@xmath10    now calculate the dissipation due to eddy currents in this .25 mm wide conductor , which will consist of transposed strands to reduce this loss @xcite .
to get an idea , take the maximum b - field during a cycle to be that generated by a 0.025 m radius conductor carrying 26000 amps . the eddy current loss in a rectangular conductor made of transposed square wires .25 mm wide ( sometimes called litz wire @xcite ) with a perpendicular magnetic field is as follows .
the width of the wire is @xmath11 and @xmath12 tesla .
@xmath13}{{(2\pi\,f\,b\,w)^2}\over{24\rho } } = [ 4 \ .05 ^ 2 \ 53]\ , { { ( 2\pi \ 4600 \ .2 \ .00025)^2 } \over { ( 24)\,1.8\times{10^{-8 } } } } = 2800 \ \hbox { kilowatts}\ ] ]    multiply by 18 magnets and divide by a duty factor of 300 to get an eddy current loss in the copper of 170 kilowatts .
stainless steel water cooling tubes will dissipate a similar amount of power @xcite .
alloy titanium cooling tubes would dissipate less .
do the eddy current losses @xcite in the 100 micron thick iron laminations .
take a quarter meter square area , a 26.5 meter length , and an average field of 1.1 tesla .
@xmath14}{{(2\pi\,f\,b\,t)^2}\over{24\rho } } } =   [ ( 26.5 ) \ , \ , ( .5 ^ 2)]\ , { { ( 2\pi \ 2600 \ 1.1 \ .0001)^2 } \over { ( 24)\,47\times{10^{-8 } } } } =   5900 \ \hbox { kw}\ ] ]    multiply by 18 magnets and divide by a duty factor of 300 to get an eddy current loss in the iron laminations of 350 kilowatts or 700 watts / m of magnet .
so the iron will need some cooling .
the ring only ramps 30 time per second , so the @xmath15 hysteresis losses will be low , even more so because of the low coercive force , h@xmath16 , of grain oriented silicon steel .
the low duty cycle of the neutrino factory leads to reasonable eddy current losses in a 4600 hz ring .
muon survival is 83% . the high permeability of grain oriented silicon steel permits high fields with little energy stored in the yoke .
gradients are switched within dipoles to minimize eddy current losses in ends .
time dilation allows extra orbits with little muon decay at the end of a cooling cycle .
this allows one to use more of the stored rf energy .
much of the magnetic field in our lattice is used for focusing rather than bending the muon beam .
more muon cooling would lead to less focusing , more bending , and an even smaller ring .
this work was supported by the u.  s.  dept .  of energy and national science foundation .
many thanks to k.  bourkland , s.  bracker , c.  jensen , s.  kahn , h.  pfeffer , g.  rees , y.  zhao , and m.  zisman for their help and suggestions .
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a 4600 hz fast ramping synchrotron is explored as an economical way of accelerating muons from 4 to 20 gev / c for a neutrino factory . 
 eddy current losses are minimized by the low machine duty cycle plus thin grain oriented silicon steel laminations and thin copper wires . 
 combined function magnets with high gradients alternating within single magnets form the lattice we describe . 
 muon survival is 83% .    
 4th nufact workshop ( neutrino factories based on muon storage rings ) , london , uk , 1 - 6 jul 2002