Time Intervals of the Energy Emission in Quantum Systems Obtained from the Conservation Rule of the Electron Momentum

The paper presents a non-probabilistic approach to the time interval associated with the energy emission produced by the electron transition in a quantum system. The calculations were performed for the hydrogen atom and the electron particle in a one-dimensional potential box. In both cases, the rule of conservation of the electron momentum has been applied. The results, limited to the time intervals of transitions between two neighbouring quantum energy levels, occur to be much similar to those obtained earlier with the aid of the Joule-Lenz energy emission theory.

Time Quanta Present in Simple Quantum Systems

Differences of the time periods in two independent quantum systems are examined on a semiclassical level. The systems are the electron in the hydrogen atom and a free-electron particle moving in a one-dimensional potential box, respectively. It is demonstrated that in both systems the relativistic correction to the time interval can be expressed as a multiple of the same quantum of time. The size of the quantum is proportional to the ratio of the Planck’s constant and the rest energy of the electron particle.

Emission Intensity in the Hydrogen Atom Calculated from a Non-Probabilistic Approach to the Electron Transitions

Quantum aspects of the Joule-Lenz law for the transmission of energy allowed us to calculate the time rate of energy transitions between the quantum states of the hydrogen atom in a fully non-probabilistic way. The calculation has been extended to all transitions between p and s states having main quantum numbers not exceeding 6. An evident similarity between the intensity pattern obtained from the Joule-Lenz law and the corresponding quantum-mechanical transition pro-babilities has been shown.

Semiclassical and Quantum-Mechanical Formalism Applied in Calculating the Emission Intensity of the Atomic Hydrogen

The energy spectrum of the hydrogen atom has been applied in calculating the time rate of energy transitions between the quantum states of the atom. The formal basis of the approach has been provided by the quantum properties of energy and time deduced from the Joule-Lenz law. The rates of the energy transitions obtained in this way were compared with the quantum-mechanical probabilities of transitions calculated earlier by Bethe and Condon and Shortley for the same pairs of the quantum states.

Time Intervals of the Electron Transitions between the Energy States in the Hydrogen Atom Calculated in a Non-Probabilistic Way

Definitions of the mechanical parameters entering the Bohr model of the hydrogen atom allowed us to calculate the time intervals connected with the electron transitions between the nearest-neighbouring energy levels in the atom. This is done in a strictly non-probabilistic way. The time results are compared with those derived earlier on the basis of the classical Joule-Lenz law for the energy emission adapted to the case of the electron transfer in the quantum systems. A similar formalism has been next applied to the harmonic oscillator and a particle moving in the one-dimensional potential box.

On the Time Fractional Modulation for Electron Acoustic Shock Waves

Nonlinear features of electron-acoustic shock waves are studied. The Burgers equation is derived and converted to the time fractional Burgers equation by Agrawal＇s method. Using the Adomian decomposition method, the shock wave solutions of the time fractional Burgers equation are constructed. The effect of time fractional parameter on the shock wave properties in auroral plasma ＆ investigated.

Time of the Energy Emission in the Hydrogen Atom and Its Electrodynamical Background

The time of the energy emission between two neighbouring electron levels in the hydrogen atom has been calculated first on the basis of the quantum aspects of the Joule-Lenz law, next this time is approached with the aid of the electrodynamical parameters characteristic for the electron motion in the atom. Both methods indicate a similar result, namely that the time of emission is close to the time period of the electromagnetic wave produced in course of the emission. As a by-product of calculations, the formula representing the radius of the electron microparticle is obtained from a simple combination of the expressions for the Bohr magnetic moment and a quantum of the magnetic flux.

Relativistic Reduction of the Electron-Nucleus Force in Bohr’s Hydrogen Atom and the Time of Electron Transition between the Neighbouring Quantum Energy Levels

The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.

Scaling Properties of Runaway Electrons

Runaway electrons in tokamaks have been widely studied theoretically and experimentally. The runaway confinement time τ1 in ohmic and additionally heated tokamak plasmas presents an anomalous behavior when compared with theoretical predictions based on neoclassical models. Runaway electrons have received lately a great attention due to several reasons： （a） the possibility to study electromagnetic turbulence by measuring the runaway flux fluctuations and its energy spectra, and （ b ） the runaway electrons are powerful diagnostics capable of yielding valuable information on the actual distribution function of fusion experiments.

Study of time resolution by digital methods with a DRS4 module

A new Digital Pulse Processing（DPP） module has been developed, based on a domino ring sampler version 4 chip（DRS4）, with good time resolution for La Br3 detectors, and different digital timing analysis methods for processing the raw detector signals are reported. The module, composed of an eight channel DRS4 chip, was used as the readout electronics and acquisition system to process the output signals from XP20D0 photomultiplier tubes（PMTs）. Two PMTs were coupled with La Br3 scintillators and placed on opposite sides of a radioactive positron22 Na source for 511 ke V γ-ray tests. By analyzing the raw data acquired by the module, the best coincidence timing resolution is about 194.7 ps（FWHM）, obtained by the digital constant fraction discrimination（d CFD） method,which is better than other digital methods and analysis methods based on conventional analog systems which have been tested. The results indicate that it is a promising approach to better localize the positron annihilation in positron emission tomography（PET） with time of flight（TOF）, as well as for scintillation timing measurement,such as in TOF-？E and TOF-E systems for particle identification, with picosecond accuracy timing measurement.Furthermore, this module is more simple and convenient than other systems.

GaN based transfer electron and avalanche transit time devices

A new model is developed to study the microwave/mm wave characteristics of two-terminal GaNbased transfer electron devices（TEDs）,namely a Gunn diode and an impact avalanche transit time（IMPATT） device.Microwave characteristics such as device efficiency and the microwave power generated are computed and compared at D-band（140 GHz center frequency） to see the potentiality of each device under the same operating conditions.It is seen that GaN-based IMPATT devices surpass the Gunn diode in the said frequency region.