Beam quality preservation and power
considerations
Sergei Nagaitsev
Fermilab/UChicago
14 October 2015
PWFA Potentials
• Large accelerating fields of about 10 GV/m in the plasma cell
and about 1 GV/m effective average field along the linac,
• Strong transverse focusing (MT/m) for accelerated electrons
supported by accelerating wave itself
• Smaller overall facility footprint dominated by the beam
delivery systems with short linacs (1.5 km/linac at 3 TeV),
• Wide range of colliding beam energy from Higgs factory to
multi-TeV.
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S. Nagaitsev | Beam quality preservation and power considerations
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Introduction (actually, these are our opinions)
• To compete with ILC or CLIC designs, a plasma-based
concept needs to achieve a luminosity of ~2x1034 at ~1 TeV
c.m.
• The upper energy for an electron-positron collider, ~3 TeV, is
limited by beamstrahlung (not by accelerating technology).
• We should keep in mind that particle physicists are asking for
an electron-positron collider, NOT electron-electron. Thus, it
is important for a plasma-based concept to work equally well
for both electrons and positrons.
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• The question is: can we achieve the luminosity of
>1034 cm-2s-1?
– With reasonable assumptions about cost, power, etc.
• Opinions in accelerator community vary
– There are both fundamental and technical challenges
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Beam-based vs. laser-based
• There is some misconception (at least among non-experts)
that beam-based plasma acceleration concepts are different
from laser-based
• Actually, the physics of particle acceleration in plasma is
largely independent of the driver.
• Opinion: Laser-based concepts offer more advantages
– More flexibility with transverse and long. laser pulse shaping.
– Huge opportunity for cost reduction because of commodity laser
market;
– Con: large number of accelerating plasma sections
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S. Nagaitsev | Beam quality preservation and power considerations
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Quasi-linear regime vs “Bubble” (a.k.a blow-out) regime
• These two regimes apply to the trailing beam, not the drive
beam.
Quasi-linear
nb  ne
suitable for both e- and e+
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S. Nagaitsev | Beam quality preservation and power considerations
Bubble
ne  0
Suitable for e-,
not suitable for e+
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Main challenge for collider applications
• How to make plasma acceleration efficient (in terms of power
transfer to the trailing beam),
– while maintaining beam parameters suitable for a collider
application (small emittance and energy spread)
Multi-TeV Linear Colliders challenges
e-
e+
source
main linac
beam delivery
Energy reach
Luminosity
Limitation by practicalities:
Wall plug power: mitigation power to beam transfer efficiency
Wall plug power <300MW @ 3TeV,
Wall plug to beam
L0.01 = 2.1034
20 MW/beam
efficiency > 13%
Cost : mitigation by high accelerating gradient
Total extension < 10km @ 3TeV
Effective Accelerating
Each linac < 2.5 km
Gradient ~ 1 GV/m
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S. Nagaitsev | Beam quality preservation and power considerations
J.P.Delahaye @ MIT April 11,2013
10/14/2015
Acceleration in ILC cavities
• The ILC cavity: ~1 m long, 30 MeV energy gain; f0 = 1.3 GHz,
wave length ≈ 23 cm
• The ILC beam: 3.2 nC (2x1010), 0.3 mm long (rms); bunches
are spaced ~300 ns (90 m) apart
• Each bunch lowers the cavity gradient by ~15 kV/m (beam
loading 0.05%); this voltage is restored by an external rf
power source (Klystron) between bunches; (~0.5% CLIC)
• Such operation of a conventional cavity is only possible
because the Q-factor is >> 1; the RF energy is mostly
transferred to the beam NOT to cavity walls.
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Acceleration in plasma
• The Q-factor is very low (for high fields) – must accelerate the
bunch within one plasma wavelength of the driver!
• Cannot add energy between bunches, thus a single bunch
must absorb as much energy as possible from the wake field.
To achieve L ~1034, bunches should
have ~1010 particles (similar to ILC
and CLIC). In principle, we can
envision a scheme with fewer
particles/bunch and a higher rep
rate, but the beam loading still
needs to be high for efficiency
reasons.
M. Tzoufras et al., PRL 101, 145002 (2008)
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Efficiency of energy transfer in a quasi-linear regime
• Shaping of bunch profile can significantly reduce accelerating
voltage variations along the bunch
– Growth of accelerating voltage is compensated by growth of
decelerating force along the bunch
• The total bunch length is (60
deg. for 50% beam loading)
• Zero energy spread
• Creating such shapes with
required beam brightness is a
challenge
Longitudinal bunch density and loaded accelerating
voltage for 50% beam loading
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Two main challenges (in our opinion)
• There are more than two, but there is not enough time in this
talk to cover all of them
1. The transverse beam break-up instability
2. Acceleration of positrons
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Transverse wake in plasma
• There is no transverse wake in a uniform plasma
– However focusing of trailing particles does exist (detuning wake)
• Beam acceleration perturbs plasma density and creates an
accelerating channel and, consequently, transverse wake
• For small beam size (σb<<c/ωp) the wake field is nearly
uniform in transverse plane
– The wake-function grows almost linearly with distance
– In a logarithmic approximation it is
W  2
k p  n 
p
 max 

sin
k
s

s
ln
,
k

 p      p c
  2  n e
 min 
where σ is the rms size of plasma channel
• In the blow-out regime we can approximately write
W  2k p 3 sin  k p  s  s   ln  2  ,    k p 1
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How strong is the transverse wake?
• In a blow-out regime with 50% beam loading the wake
defocusing force at the bunch end excited by the entire bunch
displacement Δx is comparable to the plasma focusing force
at the same position Δx
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Transverse beam break-up
• Transverse wakes act as deflecting force on bunch tail
– beam position jitter is exponentially amplified
Short-range
transverse
wake
𝑍0 𝑐𝑧
𝑊⊥ 𝑧 ~ 4
𝑎
ILC
CLIC
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S. Nagaitsev | Beam quality preservation and power considerations
a ≈ 35 mm (ILC)
a ≈ 3.5 mm (CLIC)
a ~ kp-1 (PWFA)
0.02-0.04 mm
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Transverse beam stability
• Transverse wake excites the head-tail instability of convective type
– An oscillation of bunch head leads to increased bunch oscillations of
its tail
• To prevent emittance growth and achieve beam stability the BNS
(Balakin-Novokhatsky-Smirnov) criterion has to be satisfied:
– I.e. the betatron frequency along the bunch needs to be
changed so that amplitude of all particles would stay the same
d 2x
dN (s)
pc 2  eG p x(s)  e  x(s)
W (s - s)ds
ds
ds
0
s
– the only way to obtain a focusing change in the blow-out regime is a
momentum change along the bunch.
– Assuming all particles moving with the same amplitude we obtain
required variation of momentum along the bunch
p( s )
1 dN (s)
 1
W (s - s)ds

p0
Gp 0 ds
s
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CLIC strategy: BNS damping + µm alignment of cavities
This strategy is very
challenging for PWFA
because for ~1010
particles it requires
>50% energy spread
along the bunch to
make it stable
(in a bubble regime).
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S. Nagaitsev | Beam quality preservation and power considerations
Dependence of particle momentum along
bunch required for BNS stability in blow-out
regime: beam loading 50%, longitudinal
density is adjusted to the one required for
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beam loading compensation
(see slide 11)
Strategy was also used at the SLC…
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Beam breakup in various collider proposals
• ILC
– Not important; bunch rf phase is selected to compensate for
long wake and to minimize the momentum spread
• CLIC
– Important; bunch rf phase is selected to introduce an energy
chirp along the bunch for BNS damping (~0.5% rms). May
need to be de-chirped after acceleration to meet final-focus
energy acceptance requirements
• PWFA
– Critical; BNS damping requires energy chirp comparable to
beam loading. De-chirping and beam transport is very
challenging.
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Beam loading and BNS damping
• Beam loading and the transverse beam stability are closely
coupled:
– higher beam loading requires higher energy spreads along the
bunch to keep the bunch transversely stable (by BNS damping).
– Consequence of Panofsky-Wenzel theorem
• In a bubble regime (where focusing forces are the strongest)
the transverse bunch stability requires energy spread
comparable to beam loading: 50% beam loading requires
~50% energy spread (in a linear BNS theory)
• Conclusion: New ideas are needed on how to make the beam
stable for high beam loading (and high power efficiency).
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Positrons
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Acceleration of positrons
• Acceleration of positrons is possible (in principle) in a quasilinear regime ( nb  ne)
– Challenging for colliders: Coulomb scattering leads to high
emittances (V. L. and S. N., PRST-AB 16, 108001 (2013))
• In a regime of dense positron bunches, nb  ne , the plasma
electrons get pulled into the positron bunch and create highlynonlinear focusing
A trajectory of a plasma electron
inside of the positron bunch (4x109)
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S. Nagaitsev | Beam quality preservation and power considerations
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S. Nagaitsev | Beam quality preservation and power considerations
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Challenges with a hollow-plasma channel
• Unclear how to make a channel without plasma and gas
• Transverse beam break-up is more severe because there is
no plasma focusing (like in a bubble regime).
– The effect has been known since 1999
Growth length:
5 mm for 1 pC
(~107 particles)
for ext. focusing
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Opinion
• There is still no suitable (for collider) concept for
positron acceleration.
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Technical challenges with beam driver technologies
SLAC-PUB-15426
arXiv:1308.1145
• To make a cost-effective 2 x 24-MW CW beam driver requires
substantial R&D in SCRF technology
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Summary
• Plasma Wake-Field Acceleration schemes have huge
potentials in many areas, however, collider applications
remain challenging.
• Fermilab would like to help (but is presently not funded):
– Can offer expertise in conventional colliders;
– Interested in confirming (by modeling and experiments) our
findings about BNS damping vs beam loading
– Interested in positron acceleration.
• For beam-driven PWFA schemes, the cost is determined by
conventional accelerator technologies. New ideas are needed
on how to reduce it.
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