“…The energy gain in a beam-driven plasma wave is given by the transformer ratio R = Ay/yd nvc , where Ay is the energy gained by an electron at the peak of the accelerating field and yd nve is the energy in the drive bunch Under general considerations [21], R < 2 for plasma waves driven by symmetric beams Higher transformer ratios may be achieved by using asymmetric beams to drive the wake In particular, transformer ratios with R > 2 can be achieved using a long (k p L ^$> 1), ramped beam (l e , triangular bunch with low density at the head), or, equivalently, a train of bunches with increasing charge A higher transformer ratio enables a more compact accelerator via the use of lower energy drive beams (potentially produced from smaller conventional accelerators) Appropriately shaped ramped bunches have been produced experimentally [22], as well as ramped bunch trains [23] Experiments using a ramped bunch train in a dielectric-loaded wakefield accelerator have demonstrated high transformer ratios [24] One limitation with using long beams for high transformer ratios, is that long beams are subject to instabilities, and, in particular, the electron-hose instability [25,26] The growth rate of the electron-hose instability scales as Those ~ Yb {®ptyi i {k p L) 2 l 7 ', indicating that the most effective way to suppress hosing is to reduce the bunch length In a laser plasma accelerator, the energy gam is limited by the laser energy depletion length The laser depletion length [27], for fixed laser intensity, scales as Lj <* «~3/ 2 Since, for fixed intensity, the accelerating field of the plasma wave scales as E z ~ EQ <* n l l 2 , the energy gam in a single laser-plasma accelerator scales with plasma density as Ay ~ E Z LJ <X n~x Achieving higher energy gains in a single laser-plasma accelerator requires going to lower density, lower gradient, and longer interaction lengths Present laser-plasma accelerator experiments typically rely on selftrapping of plasma electrons The self-trapping threshold is determined by the phase velocity of the plasma wave [28] In contrast to beam-driven plasma waves, the phase velocity of the laser-driven plasma wave is a function of plasma density, and for fixed intensity, the Lorentz factor of the phase velocity scales as y p w (Oo/(O p <* n l ' 2 , where G)o = 2KC/XQ IS the laser frequency Hence, to achieve high energy gains requires operating at low plasma density, and, as a consequence of the increased phase velocity, using some form of triggered injection Several methods of trigged injection are actively being explored, such as colliding pulse injection [29,30], using plasma density gradients [31,32], and ionization injection [33][34][35][36] DRIVER PROPAGATION AND COUPLING Plasma-based acceleration can be limited by the laser-plasma or beam-plasma interactio...…”