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Advanced accelerator research with focus on plasma wakefield acceleration, University of Oslo, Erik Adli, University of Oslo, August 2014,

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Luminosity Energy reach Typical accelerator gradient G~10 MV/m -> L~100 km site for 1 TeV collisions From energy reach: large accelerating gradient with low breakdown rate Beam acceleration: ~10 MW of beam power with high gradient and high efficiency (>~10%) From luminosity requirements: Low energy spread (<1%) and exellent beam emittance preservation (~<10 nm) Physics requirements for a future e+ e- collider: E cm ~ 1 TeV and L ~ /cm 2 /s Main motivation: future HEP machines

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Novel Two-Beam Acceleration Scheme Cost effective, reliable, efficient Single tunnel, no active power components Modular, staged energy upgrade High acceleration gradient: > 100 MV/m “Compact” collider: total length < 50 km at 3 teV Normal conducting acceleration structures at high RF frequency (12 GHz) CLIC main linac structure : 12 GHz Cu TW 100 MV/m gradient (loaded) Rf pulse length: t p = 240 ns Efficiency: ~5% Emittance preservation: ~10 nm e+ e- sourcemain linac beam delivery Rf based options : CLIC and ILC CLIC data :

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High gradient (CLIC 100 MV/m) Good energy efficiency (CLIC 5-10%) Excellent emittance preservation ( ~10 nm) Small emittance generation (CLIC ~10 nm) Low energy spread (CLIC ~1%) Status: Feasible Challenging Requirements for linear collider applications

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Advanced accelerator research Cutting edge accelerator physics research. The objective is to overcome limitations in conventional rf based accelerator technology. Very high frequency normal conducting rf structures (~100 GHz - ~THz) 116 GHz structure (SLAC) Dielectric structures Laser based acceleration Plasma wakefield acceleration “DLA” (SLAC) [later slides] SiO 2 ~1,0 THz,1- 10GV/m [later slides]

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Advanced acceleration research Two examples : Key milestones in advanced accelerator research are counted in term of experimental progress. Experimental progress = ideas + funding + hard work

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Direct laser acceleration? Lawson-Woodward theorem: a particle cannot get a net energy gain if interacting with laser in free space (linear approximation). Laser technology, and achievable laser fields, is advancing rapidly. For example, for a 1 J, 100 fs laser beam focused into a spot size of 10 micron, has a maximum electric field about 40 GV/cm. Can we use this field for particle acceleration? = 0 Large particle energy gains, in straight particle trajectories, can only be achieved if material boundaries are used to confine the laser field.

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Direct laser acceleration: “System on a chip” Direct acceleration from a laser beam, in a dielectric structure. This laser beam operates at optical or near infrared wavelengths. Dielectrics show high damage threshold and low loss at those wavelength. Gradients of ~300 MV/m has been been demonstrated across a ~1 mm long structure. Potential for ultra-compact, high-repetition rate acceleration.

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Dielectric laser acc. experiment Proof of principle: laser accelerates (some) particles. Very far from an accelerator applications.

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Plasma wakefield acceleration Ideas of ~100 GV/m electric fields in plasma, using W/cm 2 lasers: 1979 T.Tajima and J.M.Dawson (UCLA), Laser Electron Accelerator, Phys. Rev. Lett. 43, 267–270 (1979) Drive a wave in plasma by the space charge field of an intense charged particle beam (beam-driven) or by the radiation pressure of an intense laser beam (laser-driven). * Typical plasma densities: /cm 3 * Length scales: p ~ um * No surface material break down Terminology: LWFA: laser wakefield accelerator PWFA: [beam-driven] plasma wakefield accelerator

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Field scales in blown-out plasmas Scale of electrical fields : n 0 ~ 1e17/cm3 : E WB = 30 GV/m Scale of radial focusing forces : Strong plasma response: all plasma electrons blown-put. A perfect ion focusing channel remains. We call this the blow-out Regime. To be studies in detail later. "Acceleration and Focusing of Electrons in Two- Dimensional Nonlinear Plasma Wake-fields'', J. B. Rosenzweig (UCLA), Phys. Rev. A -- Rapid Comm. 44, R6189 (1991). Apply Gauss’ law: Wave solutions: Gauss’ law: n 0 ~ 1e17/cm3 : F r /c ~ MT/m Quadrupolar r-focusing. n 0 : plasma density E WB : “wave breaking field” – the field scale in PWFA

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Beam-driven plasma-wake field acceleration Features of beam-driven plasma wakefield acceleration (PWFA) : Plasma wave/wake excited by relativistic particle bunch Wake extracts energy from driver bunch Trailing witness bunch extracts energy from wake Quadrupolar r focusing fields (x and y) within bubble Beam-cavity alignment is not an issue Typical values: E>10 GV/m, n p ~10 17 /cm 3, λ p ~100μm High-gradient experimentally demonstrated at SLAC FFTB (2007) : 42 GeV energy gain in 85 cm of plasma. 12

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PWFA: linear theory

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Coordinates – speed of light frame sz = s - vt x The beam travels in the s direction, with speed v. The co-moving coordinate z = s-vt is defined in a frame following the beam travelling with speed v, and gives thus the relative position inside the beam. In plasma wakefield applications, the beam is often travelling with velocity v = c. In this case the frame where z = s- ct is defined is called the speed of light frame. In plasma wakefield applications other coordinates are often use; our “s” is named “z”, and the co-moving coordinate may be defined as = ct – z. The beam travels in this case towards negative z (and/or to the left on plots). We use the above definition in this course for consistency with earlier material and with what is often used for conventional acceleration.

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Linear density equation sz = s - vt n e = n 0 n e = n 0 + n nbnb

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Linear plasma density perturbation z = s – ct [um] n / n 0 General solution of : is Example for n 0 = /cm3, σ z = 20 μm and N = 10 6, Gaussian bunch. We see n / n 0 << 1 (ok) Example from I. Blumenfeld

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One dimensional solution sz = s - vt nbnb z=0 z=- z We can fully solve the system in one dimension (z), assuming a very wide bunch and all fields in the z-direction. Let the bunch have constant surface charge density, n b = [m -2 ] from z=- z to z=0. NB: This wide-bunch 1-D scenario is most often not a good model. NB: symbols “ ”, surface charge density, and “ z”, bunch length, are unrelated.

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Two dimensional solutions Analytical expressions can be developed. Main features is that solutions are more complex and that the longitudinal and radial fields depend non-linearly on r : In the narrow beam limit, the on-axis longitudinal field becomes: Sinusoidal fields: measure of linearity of plasma wakes Example for n 0 = /cm3, σ z = 20 μm and N = 10 8, Gaussian bunch (I peak ~ 10 A). We see E z << E WB (ok)

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PWFA is driver plus witness sz = s - vt x Reminder: our objective is to accelerate a witness bunch. Keywords : Gradient Energy transfer efficiency Energy spread Emittance preservation - focusing? ?

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From W. Mori (UCLA) Linear regime : e- and e+ equivalent “QuickPIC” simulation example of linear regime : NB: focusing force non-linear in r

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Field scaling in the linear regime For Gaussian beams, the longitudinal field after a narrow bunch has passed is : Fields are maximized for the relation k p z = √2, which yields the scaling law : The scale of the accelerating field can also be written as : I.e. fields scale as N/ z if the plasma density is optimized. I.e. linear in the peak current. (peak current) (constant)

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Beam loading and efficiency A beam “placed” inside an existing wake can add energy (field) to the wake, or extract energy (field) from the wake. The latter is called beam loading. If all the energy is transferred from the wake to the witness bunch, 100% energy efficiency, it is called full beam loading. In the linear regime, beam loading in calculated simply by superposition of the fields from the driver wake and the fields from the witness beam. Constant accelerating field, flattened field, along the witness bunch gives zero energy spread. In the linear regime, there are important trade- offs between charge, energy spread, energy efficiency and gradient. We will not discuss the details here.

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Summary: linear regime Focusing and accelerating fields non-linear in r Symmetric for positive and negative charges (positrons and electrons are treated the same) Field scales with peak current Efficiency and transformer ratio limited Field size limited (linear assumptions)

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PWFA: the blow-out regime

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From linear to non-linear n b << n 0 – linear regime n b ~ n 0 – non-linear wakes n b >> n 0 – blow-out regime Figures from W. Mori (UCLA)

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Blow-out regime If the driver beam current is strong enough, the space-charge force of the driver may blow away all the plasma electrons in its path, leaving a uniform layer of ions behind. The latters assumes the ions don’t move. The plasma electronics will form a narrow sheath around the evacuated area, and be pulled back by the ion-channel after the drive beam has passed. We do not attempt to model the sheath formation nor electron trajectories in this lecture (see W. Lu’s papers) We shall see that the back of the blown-out region is ideal for plasma acceleration z = s -ct EzEz plasma electron trajectories

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Quasi-static approximation Driver is moving with speed c, and is unaffected by the plasma on the time scale the plasma electrons move. z = s – ct. Maxwell equations are in this case simplified as follows : We assume a cylindrical symmetric system with coordinaties (z, r, ). At v=c the beam has radial (E r ) and azimuthal (B ) fields only, and travels along z (j=j z ). The plasma fields set up can be longitudinal or radial (j z, j r ). This implies that there are no field components E ,B z, B r in the beam-plasma system. “Wave symmetry”

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Resulting charge-field relations Inside the fully blow-out bubble, a special case of the Panofsky-Wenzel theorem holds : The longitudinal (electric) field is given by the radial currents. For the blow- out regime, a constant E z to the plasma electron sheath; amplitude given by slope of sheath electron trajectories. The transverse fields are given by charge density. For the blow-out regime, only ions, with density n 0 remains inside the bubble, yielding radial r-focusing for electrons. Valid inside a fully blown-out bubble. The Maxwell equations with these simplifications gives directly (easily shown) :

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Blow-out regime: ideal for accelerating e- From W. Mori (UCLA) (loaded) “QuickPIC” simulation example of blow-out regime :

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Energy spread and efficiency Can not be described by field superposition in the blow-out regime. Non-linear theory shows that an ideal-shaped witness bunch can perfectly flatten the field and a bunch can be accelerated without added energy spread. Charge ratio drive to witness may be a few. High charge witness acceleration possible. High efficiencies of energy transfer from drive bunch to witness bunch shown in PIC simulations, up to 90%. M. Tzoufras et al. Phys. Rev. Lett (simulations)

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Transformer ratio 31 EdEd EaEa

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Sources of emittance growth Emittance growth due to multiple scattering in plasma Acceleration to 1 TeV in n 0 = 1e17/cm 3 -> ~ 10 um V. Lebedev and S. Nagaitsev, Emittance growth due to ion motion: not well studied. Not negligible for sub-um level emittances Positrons/protons: attracts plasma e-, repelled by ions (no r focusing). Emittance growth Possible mitigation: hollow channel plasmas? Under study.

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Summary: blow-out regime Field size easily in ~100 GV/m Fields scale with square of peak current Linear focusing in r, for electrons Accelerating fields uniform in r, for electrons Positrons behaves very differently than electron (big challenge) Energy transfer efficiency from a drive charge to witness charge can be towards 80-90% High transformers ratios (>2) possible Emittance growth a big challenge (for all regimes)

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PWFA: experiments

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The AWAKE experiment at CERN AWAKE: “A Proton Driven Plasma Wakefield Acceleration Experiment at CERN”. Idea: use CERN proton bunches with kJ energies as a PWFA driver. A 400 GeV SPS bunch is sent into a plasma source, in which it drives self-modulated wake fields with accelerating fields of about 1 GV/m over 10 meters. An e- bunch will sample the wake. Global collaboration with MPI as lead experiment partner. First beam: The low-density long beam will self-modulated and generate intense wake fields. Talk for another day

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Set-up of a plasma experiment Spectrometer y-dipole Deflecting cavity YAG Li OVENCHERENKOV e- beam -> <- W-chicane Imaging quadrupoles LANEX TW Ti:Sa laser 2 km 100 m Talk for another day The FACET PWFA experiments at SLAC

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June 2013: first two bunch acceleration results Laser off: Laser on (subsequent shot): Beam spectra at the image plane of the spectrometer June 2013: we demonstrated acceleration of a beam in plasma for the first time, with accelerating fields corresponding to 6 billion volts/meter – a factor 100 higher than convention accelerators. Talk for another day

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Conclusions

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PWFA for linear collider applications Gradient (~>10 GV/m) Efficiency (~>50%) Emittance preservation Emittance generation (~< 100 nm) Energy spread (~1%) Status: Established Current research Challenging

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Extra

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Non-linear beam loading Tzoufras et al. : beam-loading in the blow-out regime. More than 80% energy transfer efficiency possible for optimally shaped trapezoidal bunch. Flattening of the longitudinal field along the witness bunch, resulting in small energy spread. : Almost flat beam loading and good very good efficiency also possible for Gaussian witness bunches. For a given blow out radius, and a given bunch separation, z, the optimal beam loading ratio is given by the appropriate witness bunch charge, bunch length (Q WB, z,WB ). From Tzoufras et al., Physics of Plasmas, 16, (2009) 41

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