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Time-Varying Fields
Published in Ahmad Shahid Khan, Saurabh Kumar Mukerji, Electromagnetic Fields, 2020
Ahmad Shahid Khan, Saurabh Kumar Mukerji
The theory based on the above postulates agrees with experiments better than classical mechanics. This theory leads to many interesting consequences. Some of these are: Relativity of simultaneity: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion.Time dilation: Moving clocks run slower than an observer’s “stationary” clock.Relativistic mass: The mass of a moving object is larger than its value at rest.Length contraction: Objects are shortened in the direction that they are moving with respect to the observer.Mass–energy equivalence: E= mc2, energy and mass are equivalent and mutually convertible.Maximum speed is finite: No physical object, message or field line can travel faster than the speed of light in a vacuum.
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Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[atomic] Relativistic mass (m) of an object traveling with velocity v in the observer’s frame: m=m0(1/{1−(v2/c2)}), where c = 2.99792458 × 108 m/s is the speed of light in vacuum and m0 is the rest mass (classical mechanics). The coefficient (1/{1−(v2/c2)}) is defined as the mass transfer coefficient. Mass absorption coefficient
Core-Pedestal Plasma Configurations in Advanced Tokamaks
Published in Fusion Science and Technology, 2023
Ehab Hassan, C. E. Kessel, J. M. Park, W. R. Elwasif, R. E. Whitfield, K. Kim, P. B. Snyder, D. B. Batchelor, D. E. Bernholdt, M. R. Cianciosa, D. L. Green, K. J. H. Law
The electrons in the plasma are directly heated in a collision-less electron-wave interaction when launching electromagnetic waves in the range of the EC frequency. However, the ions are heated indirectly by the EC waves when they collide with the EC-heated electrons. The EC frequency is the highest (~200 GHz) compared to other RF heating methods since the period of the EC rotation is the shortest in the confined plasma. The dependence of the EC frequency on the strength of the magnetic field (which decreases radially) makes the EC heating localized in a narrow resonance zone of thickness that depends on the Doppler shift of the heating wave frequency and the relativistic mass effect of the electrons. In addition, the selection of the operating frequency of the EC waves has to consider the cutoff region where the electromagnetic waves are shielded by the plasma oscillations and/or EC motion. EC waves will be refracted as the plasma density approaches the cutoff density, but within the operating space of the ECRH and electron-cyclotron current drive (ECCD) (Refs. 57, 58, and 59). Other advantages of heating the plasma with such high-frequency waves is the independence of its penetration depth on the plasma density and temperature at the edge of the tokamak and its allowance for a low-loss power transmission due to the near-optical propagation of the EC wave energy in the plasma.60
Ejection angle and depth of photoelectrons based on the electromagnetic wave concept
Published in Journal of Modern Optics, 2021
To calculate the radius of circular motion, the mass of the electron was set at (non-relativistic), and the electronic charge was set at . If the relativistic mass is considered, then the value of the radius remains unchanged, as noted in the previous section. Table 2 shows that the radius of the circular path is a fraction of nanometres. The radius remained almost constant with respect to the frequency for a particular intensity; however, the stopping potential increased significantly. The radius clearly increased with interesting intensity for a certain frequency. The radii were approximately 0.104, 0.116 and 0.132 nm for the intensities of 251, 547 and 1547 W·m−2, respectively, as listed in Table 2. As the intensity increased, the electric and magnetic fields increased, thereby acting on the electrons with greater force. Thus, the circular paths of the electrons increase with increasing intensity at a constant frequency. This is consistent with the prediction of the EM wave concept [14,15]. The radius increased significantly with increasing frequency at a constant intensity owing to the centrifugal force of the circular motion of electrons with increasing angular velocity. A few inconsistent results were observed in radii with very small values, and this may be due to experimental error.
Absolute instability of acoustic wave in semiconductor plasma: relativistic effects
Published in Radiation Effects and Defects in Solids, 2021
Swati Dubey, S. Ghosh, Subhash Chouhan
An important field of study in nonlinear acoustics is amplification/attenuation and frequency mixing of waves in semiconductors (especially III–V semiconductors) (15–18) because of its immediate pertinence to problems of optical communication systems. When an intense pump beam is passed through the medium, it causes considerable perturbation. For higher pump fields, change in relativistic mass variation of the electron may play a significant role to modify the mobility of carriers as well as the conductivity of the medium and hence produces refinement effects. In our preceding works (19,20), it is found that nonlinear amplification and dispersion properties also get modified when the relativistic mass variation of electrons is taken into account. The inclusion of relativistic mass variation of electron thermal temperature and relative electron drift produces electron acoustic instability. This relativistic effect also affects the instability phenomena and it is hoped that it may significantly change the phase and gain profile.