Time Delay in Electron Collision with a Spherical Target as a Function of the Scattering Angle

We have studied the angular time delay in slow-electron elastic scattering by spherical targets as well as the average time delay of electrons in this process. It is demonstrated how the angular time delay is connected to the Eisenbud–Wigner–Smith (EWS) time delay. The specific features of both angular and energy dependencies of these time delays are discussed in detail. The potentialities of the derived general formulas are illustrated by the numerical calculations of the time delays of slow electrons in the potential fields of both absolutely hard-sphere and delta-shell potential well of the same radius. The conducted studies shed more light on the specific features of these time delays.

Energy convexity of intrinsic bi-harmonic maps and applications I: Spherical target

In this paper, we show an energy convexity and thus uniqueness for weakly intrinsic bi-harmonic maps from the unit 4-ball {B_{1}\subset\mathbb{R}^{4}} into the sphere {\mathbb{S}^{n}}. In particular, this yields a version of uniqueness of weakly harmonic maps on the unit 4-ball which is new. We also show a version of energy convexity along the intrinsic bi-harmonic map heat flow into {\mathbb{S}^{n}}, which in particular yields the long-time existence of the intrinsic bi-harmonic map heat flow, a result that was until now only known assuming the non-positivity of the target manifolds by Lamm [26]. Further, we establish the previously unknown result that the energy convexity along the flow yields uniform convergence of the flow.

Effects of Surface Diffuseness and Coupling Radius Parameters on The Fusion and Quasi-Elastic Barrier Distributions

We study the heavy-ion reaction at sub-barrier energies for ¹⁶O+^144,154Smsystems using full order coupled-channels formalism. We especially investigate the effect of fusion and quasi- elastic barrier distributions on the surface diffuseness and the coupling radius parameters of the nuclear potential for these systems. We found that the structure of fusion and quasi-elastic barrier distributions is more sensitive to the surface diffuseness and coupling radius parameters for the reaction with spherical target, ¹⁶O+¹⁴⁴Sm systemcompared to the reaction that involves the deformed target, i.e., ¹⁶O+¹⁵⁴Sm system. In more detail, the results of coupled-channels calculations for the fusion and the quasi-elastic barrier distributions for deformed target are not sensitive to the choice of the coupling radius and surface diffuseness parameters. In mark contrast, the structure of the fusion and the quasi-elastic barrier distributions for spherical target are very sensitive to the coupling radius and surface diffuseness parameters. We found that the small surface diffuseness parameter smeared out the fusion barrier distributions and the larger coupling radius smoothed the high energy peak of the quasi-elastic barrier distributions. We also found that the larger coupling radius, , is required by the experimental quasi-elastic barrier distribution for the ¹⁶O+¹⁴⁴Sm system whereas the experimental fusion barrier distribution compulsory the small value, i.e., .

Coriolis force-assisted inertial confinement fusion

A fundamental problem for the realization of laser fusion through the implosion of a spherical target is Kidder's E−1/6 law, where E is the energy needed for ignition, proportional to the 6th power of the ratio R/R0, where R0 and R are the initial and final implosion radii, respectively. This law implies that the ignition energy is very sensitive to the ratio R0/R, or vice versa, the ratio R0/R is very insensitive to the energy input, with R0/R limited by the Rayleigh–Taylor instability. According to still classified data of the Centurion–Halite experiment at the Nevada Test Site, ignition would require an energy of ${\rm E}\simeq 50\,{\rm MJ}$, 25 times larger than the 2 MJ laser at the National Ignition Facility (NIF) reported in the New York Times. This means that even a tenfold increase from 2 to 20 MJ would only decrease the R/R0 ratio by an insignificant factor of 10−1/6 ≃ 0.7. To overcome this problem, it is proposed that the spherical target is replaced with a hollowed-out, rapidly rotating, cm-size ferromagnetic target, accelerated by a rotating traveling magnetic wave to a rotational velocity of ~1 km/s, at the limit of its tensile strength. In a rotating reference system, the general theory of relativity predicts the occurrence of negative gravitational field masses in the center of rotation, with their source located in the Coriolis force field. The density of this negative gravitational field mass can be larger than the magnitude of the positive mass density of a neutron star. The repulsive gravitational force causes the centrifugal force. For a magnetized plasma placed in the rapidly spinning, hollowed-out target chamber, this repulsive force can be balanced by the magnetic force generated by thermomagnetic currents of the Nernst effect. Such a configuration does not suffer from the Rayleigh–Taylor instability, but becomes a small magnetohydrodynamic generator, amplifying the magnetic field to values about equal to those of the Nernst effect, axially confining the plasma. By placing the spinning target in the center of a lithium vortex, the fusion neutrons absorbed in the vortex can breed tritium, and at the same time remove heat from the target chamber to sustain the Nernst effect. A hot spot is thereby produced in the target chamber, which launches a thermonuclear burn wave into a cylindrical deuterium–tritium configuration. With the stability of a rapidly rotating target greatly increased, and the range of 10 MeV electrons in the wall of the cm-size ferromagnetic target, an intense 10 MeV relativistic electron beam drawn from a 10 MJ Marx generator should be sufficient to implode the target for thermonuclear ignition.