Muon Acceleration in a Neutrino Factory
Orbit Correction in a nonscaling FFAG
D. J. Kelliher, ASTeC, STFC Rutherford Appleton Laboratory, Harwell, Didcot, Oxfordshire, OX11 0QX
It is a requirement of the proposed Neutrino Factory (NF) that, due to their short decay time and large
emmitance, the muons are rapidly accelerated to a kinetic energy of at least 20GeV. It is proposed that this is
achieved by a chain of non-scaling Fixed Field Alternating Gradient (FFAG) accelerators. EMMA is a prototype
electron model nonscaling FFAG to be built at Daresbury. Topics examined in this poster will include the
difficulties in orbit correction due to the large transverse tune excursion in a non-scaling FFAG.
Failure of harmonic correction
Advantages of FFAG for neutrino factory
• Very rapid acceleration rate (as no synchronisation
is required between magnets and rf)
• Large acceptance (muon beam will have large
emittance)
• Reuse of rf cavities (cost-effective)
xi 
i  kick
2Sin x 
 kick Cos i  kick    
Effect of kicker varies since the phase
advance between the kicker and any point in
the lattice changes as the momentum
increases. Therefore, conventional harmonic
correction of error source with kickers is not
possible in a nonscaling FFAG.
Optimising initial conditions
Figure shows how the orbit
distortion rms depends on
the initial vertical tune (i.e.
injecting at different
momenta). In general, the
closed orbit co-ordinates at
the injection momentum
do not give optimal initial
conditions. A scan over the
initial phase space
(x,x’,y,y’) allows the
distortion to be optimised.
Latest acceleration scheme of International Scoping Study [1]
EMMA nonscaling FFAG comprises 42 shifted quadrupole
doublets. The energy range is 10-20 MeV.
Orbit distortion due to alignment errors
Many integral tunes are
crossed over the energy
range. While there are
peaks
in
closed
orbit
distortion near the integral
tunes (black curve), when
acceleration is included, this
correlation is not evident
(red
curve).
We
may
surmise that the beam does
not see the effects of
resonance,
instead
the
distortion is due to the
random kicks imparted by
the quad misalignment [2].
Local correction of magnets
It will be necessary to realign magnets to correct
misalignments. In EMMA there are horizontal
sliders on each magnet to allow for this. In the
absence of other error sources, by placing
simulated kickers in each magnet, and adjusting
their strengths until 2 is minimized, the magnet
displacements can be inferred from the BPM
measurements. The algorithm can be generalised
to include other error sources (as in the storage
ring code LOCO [3]).

 x 
x
    M  
 y
 y 
2 
nbpm

x
calculated
i
i
xmagnet 
2.
3.


2
2
i
 kick
References
1.
 ximeasured
kl
“International scoping study of a future Neutrino Factory and super-beam facility”,
www.hep.ph.ic.ac.uk/iss/
S. Machida and D.J. Kelliher, ‘Orbit and optics distortion in fixed field alternating gradient
muon accelerators’,submitted to Phys. Rev. STAB
J. Safranek, ‘Experimental determination of storage ring optics using orbit response
measurements’, Nucl. Inst. And Meth. A388, 27 (1997)
CERN accelerator school 2007, Daresbury