Inelastic Interaction and Blowup New Solutions of Nonlinear and Dispersive Long Gravity Waves

In this paper, the fractional Broer–Kaup (BK) system is investigated by studying its novel computational wave solutions. These solutions are constructed by applying two recent analytical schemes (modified Khater method and sech–tanh function expansion method). The BK system simulates the bidirectional propagation of long waves in shallow water. Moreover, it is used to study the interaction between nonlinear and dispersive long gravity waves. A new fractional operator is used to convert the fractional form of the BK system to a nonlinear ordinary differential system with an integer order. Many novel traveling wave solutions are constructed that do not exist earlier. These solutions are considered the icon key in the inelastic interaction of slow ions and atoms, where they were able to explain the physical nature of the nuclear and electronic stopping processes. For more illustration, some attractive sketches are also depicted for the interpretation physically of the achieved solutions.

COMPARISON OF GLOW, ARC, AND MAGNETRON DIRECT CURRENT DISCHARGES

Glow discharge (GD) in a tube, arc discharge (AD) without cathode heating from an external source, and magnetron discharge (MD) in a planar magnetron are compared. In each of the discharges, characteristic areas are distinguished. In MD, electrons trapped in the near-cathode region are not directly involved in ionization processes, but “wake” acceleration of slow ions by electrons that move along Larmor orbits is possible, which gives additional energy to ions moving toward the cathode. In GD in the near-cathode region, the average energy of the ejected electrons is on the order of several electron volts, and the energy of the ions and neutrals is less than 0.1 eV. In MD in the near-cathode region, the average energy of knocked-out electrons, ions, and neutrals is on the order of tens of electron volts. The differential resistance of GD is negative, that of AD is usually negative, and that of MD is positive. The energy of ions in the magnetron plasma can be greater than that of electrons, which gives new possibilities for acoustoplasma control of MD and the creation of appropriate instruments and devices.