Abstract:
Intractable epilepsy with painful partial motor seizures is a relatively rare and difficult disorder to treat. We evaluated the usefulness of botulinum toxin to reduce ictal pain. Two patients received two or four botulinum toxin (BTX) injections at one-to-two-month intervals. Patient 1 had painful seizures of the right arm and hand. Patient 2 had painful seizures involving the left foot and leg. Injections were discontinued after improved seizure control following resective surgery. Both patients received significant pain relief from the injections with analgesia lasting at least two months. Seizure severity was reduced, but seizure frequency and duration were unaffected. For these patients, BTX was effective in temporarily relieving pain associated with muscle contraction in simple partial motor seizures. Our findings do not support the hypothesis that modulation of motor end-organ feedback affects focal seizure generation. BTX is a safe and reversible treatment that should be considered as part of adjunctive therapy after failure to achieve control of painful partial motor seizures.

Abstract:
Compression of turbulent plasma can amplify the turbulent kinetic energy, if the compression is fast compared to the viscous dissipation time of the turbulent eddies. A sudden viscous dissipation mechanism is demonstrated, whereby this amplified turbulent kinetic energy is rapidly converted into thermal energy, suggesting a new paradigm for fast ignition inertial fusion.

Abstract:
The mode-converted ion-Bernstein wave excited in tokamaks is shown to exhibit certain very interesting behavior, including the attainment of very small poloidal phase velocities, the reversal of poloidal direction, and up-down asymmetries in propagation and damping. Because of these effects, this wave holds promise for channeling {$\alpha$-particle}\ power to ions, something that would make a tokamak fusion reactor far more attractive than presently envisioned.

Abstract:
The wave-particle alpha-channeling effect is generalized to include rotating plasma. Specifically, radio frequency waves can resonate with alpha particles in a mirror machine with ExB rotation to diffuse the alpha particles along constrained paths in phase space. Of major interest is that the alpha-particle energy, in addition to amplifying the RF waves, can directly enhance the rotation energy which in turn provides additional plasma confinement in centrifugal fusion reactors. An ancillary benefit is the rapid removal of alpha particles, which increases the fusion reactivity.

Abstract:
An optically thin $p$-$^{11}$B plasma loses more energy to bremsstrahlung than it gains from fusion reactions, unless the ion temperature can be elevated above the electron temperature. In thermal plasmas, the temperature differences required are possible in small Coulomb logarithm regimes, characterized by high density and low temperature. The minimum Lawson criterion for thermal $p$-$^{11}$B plasmas and the minimum $\rho R$ required for ICF volume ignition are calculated. Ignition could be reached more easily if the fusion reactivity can be improved with nonthermal ion distributions. To establish an upper bound for this utility, we consider a monoenergetic beam with particle energy selected to maximize the beam- thermal reactivity. Channeling fusion alpha energy to maintain such a beam facilitates ignition at lower densities and $\rho R$, improves reactivity at constant pressure, and could be used to remove helium ash. The gains realized with a beam thus establish an upper bound for the reductions in ignition threshold that can be realized with any nonthermal distribution; these are evaluated for $p$-$^{11}$B and DT plasmas.

Abstract:
A classical particle oscillating in an arbitrary high-frequency or static field effectively exhibits a modified rest mass m_eff derived from the particle averaged Lagrangian. Relativistic ponderomotive and diamagnetic forces, as well as magnetic drifts, are obtained from the m_eff dependence on the guiding center location and velocity. The effective mass is not necessarily positive and can result in backward acceleration when an additional perturbation force is applied. As an example, adiabatic dynamics with m_|| > 0 and m_|| < 0 is demonstrated for a wave-driven particle along a dc magnetic field, m_|| being the effective longitudinal mass derived from m_eff. Multiple energy states are realized in this case, yielding up to three branches of m_|| for a given magnetic moment and parallel velocity.

Abstract:
For a nonrelativistic classical particle undergoing arbitrary oscillations, the generalized effective potential Y is derived from nonlinear eigenfrequencies of the particle-field system. Specifically, the ponderomotive potential is extended to a nonlinear oscillator, resulting in multiple branches near the primary resonance. For a pair of natural frequencies in a beat resonance, Y scales linearly with the internal actions and is analogous to the dipole potential for a two-level quantum system. Thus cold quantum particles and highly-excited quasiclassical objects permit uniform manipulation tools, particularly, one-way walls.

Abstract:
A general nonlinear dispersion relation is derived in a nondifferential form for an adiabatic sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of trapped electrons. The linear dielectric function is generalized, and the nonlinear kinetic frequency shift $\omega_{\rm NL}$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield $\omega_{\rm NL} \propto \sqrt{a}$, as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation. Such beams are formed whenever the phase velocity changes, because the trapped distribution is in autoresonance and thus evolves differently from the passing distribution. Hence, even adiabatic $\omega_{\rm NL}(a)$ is generally nonlocal.

Abstract:
The evolution of adiabatic waves with autoresonant trapped particles is described within the Lagrangian model developed in Paper I, under the assumption that the action distribution of these particles is conserved, and, in particular, that their number within each wavelength is a fixed independent parameter of the problem. One-dimensional nonlinear Langmuir waves with deeply trapped electrons are addressed as a paradigmatic example. For a stationary wave, tunneling into overcritical plasma is explained from the standpoint of the action conservation theorem. For a nonstationary wave, qualitatively different regimes are realized depending on the initial parameter $S$, which is the ratio of the energy flux carried by trapped particles to that carried by passing particles. At $S < 1/2$, a wave is stable and exhibits group velocity splitting. At $S > 1/2$, the trapped-particle modulational instability (TPMI) develops, in contrast with the existing theories of the TPMI yet in agreement with the general sideband instability theory. Remarkably, these effects are not captured by the nonlinear Schr\"odinger equation, which is traditionally considered as a universal model of wave self-action but misses the trapped-particle oscillation-center inertia.

Abstract:
A Lagrangian formalism is developed for a general nondissipative quasiperiodic nonlinear wave with trapped particles in collisionless plasma. The adiabatic time-averaged Lagrangian density $\mcc{L}$ is expressed in terms of the single-particle oscillation-center Hamiltonians; once those are found, the complete set of geometrical-optics equations is derived without referring to the Maxwell-Vlasov system. The number of trapped particles is assumed fixed; in particular, those may reside close to the bottom of the wave trapping potential, so they never become untrapped. Then their contributions to the wave momentum and the energy flux depend mainly on the trapped-particle density, as an independent parameter, and the phase velocity rather than on the wave amplitude $a$ explicitly; hence, $\mcc{L}$ acquires $a$-independent terms. Also, the wave action is generally not conserved, because it can be exchanged with resonant oscillations of the trapped-particle density. The corresponding modification of the wave envelope equation is found explicitly, and the new action flow velocity is derived. Applications of these results are left to the other two papers of the series, where specific problems are addressed pertaining to properties and dynamics of waves with trapped particles.