Effect of plasma inhomogeneity on plasma wakefield acceleration driven by long bunches

Effects of plasma inhomogeneity on self-modulating proton bunches and accelerated electrons were studied numerically. The main effect is the change of the wakefield wavelength which results in phase shifts and loss of accelerated particles. This effect imposes severe constraints on density uniformity in plasma wakefield accelerators driven by long particle bunches. The transverse two stream instability that transforms the long bunch into a train of micro-bunches is less sensitive to density inhomogeneity than are the accelerated particles. The bunch freely passes through increased density regions and interacts with reduced density regions.Comment: 7 pages, 10 figure

A theory of thin shells with orbiting constituents

The self-gravitating, spherically symmetric thin shells built of orbiting particles are sstudied. Two new features are found. One is the minimal possible value for an angular momentum of particles, above which elleptic orbits become possible. The second is the coexistence of both the wormhole solutions and the elleptic or hyperbolic orbits for the same values of the parameters (but different initial conditions). Possible applications of these results to astrophysics and quantum black holes are briefly discussed.Comment: 22 pages, Latex, 10 eps figures. CERN preprint no. CERN-TH 2000-16

Dynamics of a thin shell in the Reissner-Nordstrom metric

We describe the dynamics of a thin spherically symmetric gravitating shell in the Reissner-Nordstrom metric of the electrically charged black hole. The energy-momentum tensor of electrically neutral shell is modelled by the perfect fluid with a polytropic equation of state. The motion of a shell is described fully analytically in the particular case of the dust equation of state. We construct the Carter-Penrose diagrams for the global geometry of the eternal black hole, which illustrate all possible types of solutions for moving shell. It is shown that for some specific range of initial parameters there are possible the stable oscillating motion of the shell transferring it consecutively in infinite series of internal universes. We demonstrate also that this oscillating type of motion is possible for an arbitrary polytropic equation of state on the shell.Comment: 17 pages, 7 figure

The wave function of a gravitating shell

We have calculated a discrete spectrum and found an exact analytical solution in the form of Meixner polynomials for the wave function of a thin gravitating shell in the Reissner-Nordstrom geometry. We show that there is no extreme state in the quantum spectrum of the gravitating shell, as in the case of extreme black hole.Comment: 7 pages, 1 figur

Quantum geometrodynamics for black holes and wormholes

The geometrodynamics of the spherical gravity with a selfgravitating thin dust shell as a source is constructed. The shell Hamiltonian constraint is derived and the corresponding Schroedinger equation is obtained. This equation appeared to be a finite differences equation. Its solutions are required to be analytic functions on the relevant Riemannian surface. The method of finding discrete spectra is suggested based on the analytic properties of the solutions. The large black hole approximation is considered and the discrete spectra for bound states of quantum black holes and wormholes are found. They depend on two quantum numbers and are, in fact, quasicontinuous.Comment: Latex, 32 pages, 5 fig

Natural noise and external wake field seeding in a proton-driven plasma accelerator

We discuss the level of natural shot noise in a proton bunch-driven plasma accelerator. The required seeding for the plasma wake field must be larger than the cumulative shot noise. This is the necessary condition for the axial symmetry of the generated wake and the acceleration quality. We develop an analytical theory of the noise field and compare it with multi-dimensional simulations. It appears that the natural noise wake field generated in plasma by the available at CERN super-protons-synchrotron (SPS) bunches is very low, at the level of a few 10 kV/m. This fortunate fact eases the requirements on the seed. Our three dimensional simulations show that even a few tens MeV electron bunch precursor of a very moderate intensity is sufficient to seed the proton bunch self-modulation in plasma.Comment: 5 pages, 5 figure

Zel'dovich states with very small mass and charge in nonlinear electrodynamics coupled to gravity

It is shown that in non-linear electrodynamics (in particular, Born-Infeld one) in the framework of general relativity there exist "weakly singular" configurations such that (i) the proper mass M is finite in spite of divergences of the energy density, (ii) the electric charge q and Schwarzschild mass m ~ q can be made as small as one likes, (iv) all field and energy distributions are concentrated in the core region. This region has an almost zero surface area but a finite longitudinal size L=2M. Such configurations can be viewed as a new version of a classical analogue of an elementary particle.Comment: 11 pages. 1 reference added. To appear in Grav. Cosm

On the variational principle for dust shells in General Relativity

The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on the shell. These conditions and the gravitational field equations which follow from an initial variational principle, are used for elimination of the gravitational degrees of freedom. The transformation of the variational formula for spherically-symmetric systems leads to two natural variants of the effective action. One of these variants describes the shell from a stationary interior observer's point of view, another from the exterior one. The conditions of isometry of the exterior and interior faces of the shell lead to the momentum and Hamiltonian constraints. The canonical equivalence of the mentioned systems is shown in the extended phase space. Some particular cases are considered.Comment: 25 pages, RevTeX, no figures, revised version, typos corrected, accepted for publication in Journal of Mathematical Physic

Single State Supermultiplet in 1+1 Dimensions

We consider multiplet shortening for BPS solitons in N=1 two-dimensional models. Examples of the single-state multiplets were established previously in N=1 Landau-Ginzburg models. The shortening comes at a price of loosing the fermion parity $(-1)^F$ due to boundary effects. This implies the disappearance of the boson-fermion classification resulting in abnormal statistics. We discuss an appropriate index that counts such short multiplets. A broad class of hybrid models which extend the Landau-Ginzburg models to include a nonflat metric on the target space is considered. Our index turns out to be related to the index of the Dirac operator on the soliton reduced moduli space (the moduli space is reduced by factoring out the translational modulus). The index vanishes in most cases implying the absence of shortening. In particular, it vanishes when there are only two critical points on the compact target space and the reduced moduli space has nonvanishing dimension. We also generalize the anomaly in the central charge to take into account the target space metric.Comment: LaTex, 42 pages, no figures. Contribution to the Michael Marinov Memorial Volume, ``Multiple facets of quantization and supersymmetry'' (eds. M.Olshanetsky and A. Vainshtein, to be publish by World Scientific). The paper is drastically revised compared to the first version. We add sections treating the following issues: (i) a new index counting one-state supermultiplets; (ii) analysis of hybrid models of general type; (iii) generalization of the anomaly in the central charge accounting for the target space metri

Mass of perfect fluid black shells

The spherically symmetric singular perfect fluid shells are considered for the case of their radii being equal to the event horizon (the black shells). We study their observable masses, depending at least on the three parameters, viz., the square speed of sound in the shell, instantaneous radial velocity of the shell at a moment when it reaches the horizon, and integration constant related to surface mass density. We discuss the features of black shells depending on an equation of state.Comment: 1 figure, LaTeX; final version + FA