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On the size of TeV laser-plasma accelerators Multistaging

On the size of TeV laser-plasma accelerators Multistaging. Goal: Put numbers, orders of magnitude on TeV acceleration: size, laser Trigger a discussion on staging Model: very simple, 0 order model: Linear Wakefield Theory: good for engineering, more stable,

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On the size of TeV laser-plasma accelerators Multistaging

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  1. On the size of TeV laser-plasma accelerators Multistaging • Goal: • Put numbers, orders of magnitude on TeV acceleration: size, laser • Trigger a discussion on staging • Model: very simple, 0 order model: • Linear Wakefield Theory: good for engineering, more stable, • more robust, easy to calculate and easy to scale • 1D (OK if channel focusing electric field is high enough) • or results have to be modified by a factor of 2 • linear : dn/n ~ 0.3 (limit of linear regime) • only 1 electron • no pump depletion

  2. Equations of motion in 1D plasma wave Initial conditions: p0, 0

  3. Single stage TeV accelerator: trapped orbit Phase space trajectory (dn/n=0.3) 1 TeV  ne=6.5×1014 cm-3

  4. Single stage TeV accelerator: km length From 100 GeV to 1 TeV: acceleration distance is 2 km

  5. Single stage TeV accelerator: parameters Accelerator LASER guided unguided (rayleigh length) Energy conservation consideration: 1 nC @ 1 TeV ~ 1 kJ 10% efficiency Elaser > 10 kJ 40 m diameter beam !! f=1000 km !!

  6. The limit of accelerating on trapped orbits Emax • Emax is given by separatrix: large Emax  low density plasma • long dephasing length • low accelerating gradient • last acceleration stage always at low density

  7. accelerating on untrapped orbits If ginj > gp and gp >> 1, then max gain on untrapped orbit is given by Example: from 10 to 20 GeV 10 GeV gain Injection at 10 GeV • No limit to Emax • Higher density OK • Higher gradients • Reduces size

  8. Example: a 10 GeV-20 GeV stage Trapped orbit with Emax=20 GeV 3 m for 10 GeV gain Untrapped orbit with Emax=10 GeV 2 m for 10 GeV gain

  9. Multistaging to 1 TeV using untrapped orbits • First stage= 1 GeV – few centimeters few ne=1018 cm-3 • N identical stages (optimal case for this model using untrapped orbits) Gain per stage is So the density of a single stage is Dephasing length per stage Total accelerator length

  10. Scaling for a multistage 1 TeV accelerator l=1 µm, a0=0.8, resonant plasma wave, dn/n=0.3

  11. Some questions • Pulse deformation time (longitudinal) given by RFS growth rate: • always much smaller than propagation time: onset of nonlinearities • HOW DO WE MODEL LONG PROPAGATION LENGTHS ? • Pump depletion: • - can be neglected when a02 << 1. • - pump depletion length compare with dephasing length for a02 >> 1 • - no scaling for a0 ~ 1 • HOW DO WE MODEL LONG PROPAGATION LENGTHS ? • Further questions: • Other schemes for staging ? • Look at similar problem with the beam-plasma accelerator • What comes between the stages ? Focusing optics, magnets …

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