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11PHYSICAL SCIENCES
MOTION OF CHARGED PARTICLES IN THE FIELD OF WAVE PACKETS IN CROSSED ELECTRIC AND MAGNETIC FIELDS, CONSIDERING WEAKLY RELATIVISTIC EFFECTS
Karnilovich S., Shaar Y., Hassan N.
Associate professors Institute of Physical Research and Technology Russian University of Peoples' Friendship - Moscow
Abstract
In this work we considered was constructed the theory of motion of charged particles in the field of wave packets in crossed electric and magnetic fields, taking into account weak relativistic effects.
Keywords: Motion of charged particles, Acceleration of charged particles, wave packets.
Drift theory of motion of charged particles in electromagnetic fields, determine two cases: a "weak" electric field when the electric drift velocity is VE~eV, and a "strong" electric field when VE~V , Here V is the characteristic particle velocity, £ is a small parameter equal to the ratio of the particle gyroradius to the characteristic scale of the inhomogeneity of a strong magnetic field, even in the nonrelativistic approximation, the case of a strong electrostatic field is complicated and full of difficulties [2]. In [2-4], taking into account weakly relativistic effects, was constructed the theory of motion of charged particles in the field of wave packets in crossed electric and magnetic fields.
If the speed of electric drift is not constant, but is a function of the coordinates and time, then the transition to the corresponding system moving with the speed of electric drift leads to certain difficulties, since such a system is non-inertial.
This paper proposes an approach to solve this problem. It is assumed that the electric drift velocity is very less than the speed of light in vacuum. Such a proposal is quite sufficient to solve many applied problems. The equations of motion averaged over fast oscillations of the relativistic charged particle are obtained taking into account the effects of quasistationary electric drift.
(E(r ,t) = E0(r ,t)+EHF(r ,t) W ,t) = B0(r ,t) + BHF(r ,t)
(1)
Where
JHF
Introducing
EHP(r ,t) = \eiQ + k.c. BHF(r ,t) = $eiQ +k.c.
(2)
ei =■
= 1
e^r ,t),e2(r ,t),e3(r ,t) (3)
_Ba_
The fast phase is described by the equation will be
p2 , e-i
dt dt dt
(4)
Let us single out the cyclotron rotation of the particle and the electric drift VE using the formula:
P = PE + e1P]] + ^ (e2. -e™0 + e3. +e-»0) (5)
Where Q0 - is the gyrophase, PE = m0rVE m0- is the mass of the particle,
M , r = (l + ^Y/2 - the rda-
tivistic factor.
e± = e2 ± i§3 The equation of motion of a relativistic charged particle q:
dP ;},-» . q
— = qE(r , t) +--— [P, B]
dt macV L J
(6)
Substituting expressions (1) and (5) into equation (6) and projecting onto the directions e1 , 1(e-el0° +
e+e-l9°) h ^ (e-el9° — e+e~w°), we obtain the exact equations in the form
(7)
(8)
Where £ - is the small parameter, x = (r, Pu,P±) -is the vector of slow variables, Q = (Q0, Q) - is the vector of fast variables containing the gyro phase and phase of the waves (2),
n0 qB0
% = f(t.*.Q.e)
^ = lu(t,x)+A(t,x,Q,£)
r m„cT
- relativistic cyclotron frequency,
(l + ±d)/2 \ m0c )
p.,
v = -m + kz-^ - Doppler shift frequency, y =
Where ra is the local frequency k - is the local wave vector, Q is the fast phase.
m0c
The equations obtained are valid only for quasi-longitudinal wave propagation, when the particle gyro-radius is small compared to the transverse wavelength [6]
K±r~£ (9)
Then making transition to a new phase (since the gyroradiusrelat of the particle is not small, Kr~1), by the formula:
^ = Q--ZT^e&Sin^o-e3Cos%) (10)
mniin
Averaging the resulting system of equations over all fast phases, except for the phase of demultiplication resonance, where is the resonant phase: ^res = 2tp0 +
Q and 2m0 + v = 0 , we obtain a system of equations for waves of arbitrary polarization in a dimensionless form:
p-l = B-0Pty2Coscp
dr
= -1-
1(2
dr 2a0 , P\ yœ
P* 2y2
pwpi
PI'P±-L-L
u*
£1 = £xCoS& = £ySin&
® = tyres ~tyV\\ =
-t = œt a = —
m0vc œ
(11) (12) ) Cos(p (13)
dJyT = Ê°p±.Cos(p(PPyi+(V, + V\\)tg(p) (14)
Ve1£±
This resonance is a consequence of relativism and is possible only in the presence of a strong electrostatic field.
REFERENCES:
1. V.P. Milantiev TECHNICAL PHYSICS LETTERS - 1994 64 p. 166
2. S.P. Karnilovich, V.P. Milantiev Journal of Experimental and Theoretical Physics - 1989; P. 95
THE PHYSICS OF IMAGINARY NUMBERS IS THE NEW PHYSICS, IT IS PHYSICS OF AN INVISIBLE, BUT REALLY EXISTING WORLD
Antonov A.
Ph.D, HonDSc, HonDL, H.ProfSci, ResProf, Independent Researcher, Kiev, Ukraine
Abstract
It is quite clear that the discovery of invisible universes is an outstanding and far more significant event than even the discovery of America by Columbus. However, their discovery is hampered not only by the objective difficulties of knowledge nature, but also by the principle of non-exceeding the speed of light of the special theory of relativity (STR), from which the existence of only our visible universe follows. But in the XXI century, experimental knowledge was obtained, from which it followed that the relativistic formulas of the existing version of STR are incorrect and incorrectly explained. In other words, the version of STR created in the 20th century turned out to be not entirely correct. Therefore, an alternative version of S STR RT was created, which made it possible to prove the existence, in addition to our visible universe, of other mutually invisible universes. It is explained how these invisible universes can be seen. But invisible universes are not the only invisible objects that actually exist in nature, which are described by imaginary numbers. Other real-life invisible physical objects correspond to other imaginary numbers. Therefore, the physics of imaginary numbers is the physics of the still largely unknown invisible world. STR
Keywords: imaginary numbers; special theory of relativity; dark matter; dark energy; dark space; Multiverse; Hyperverse, invisible universes.
1. Introduction
What could be the physical sense of imaginary numbers? It has remained completely incomprehensible until very recently, unlike the sense of other numbers, such as integer and fractional, positive and negative, rational and irrational, etc, which became clear immediately after their discovery. Even today no one can
explain what is, for example, 51 kilograms, 71 seconds
or 21 meters, where i = is the imaginary unit, although imaginary numbers were discovered by Scipione del Ferro, Niccoló Fontana Tartaglia, Gerolamo Car-dano, Lodovico Ferrari and Rafael Bombelli [1] about five hundred years ago. And perhaps even earlier this scientific discovery was made by Paolo Valmes [2], who was sentenced to death at the stake by Spanish inquisitor Tomás de Torquemada for this discovery. Therefore, even Sir Isaac Newton had to regard the opinion of the Inquisition about imaginary numbers and preferred not to use1 them in his writings.
Moreover, physical sense of imaginary numbers has remained so incomprehensible until very recently as to prevent creation of the special theory of relativity (STR) in the 20th century, although it is generally believed to have been already created. And it is even presented in all university and school physics textbooks. But this generally acknowledged version of STR is not entirely correct2, since the relativistic formulas obtained in it are incorrect, they are incorrectly explained using the incorrect principle of light speed non-exceed-ance, and also from them incorrect conclusions are made about the physical unreality of imaginary numbers and the existence in nature only of our visible Universe.
Imaginary numbers are actually shown below to be physically real. And while the physics of real numbers corresponds to the world we see, the physics of imaginary numbers corresponds to the invisible (moreover, also not otherwise tangible) and therefore largely unexplored world.
1 In the atmosphere of Inquisition's omnipotence and intolerance of unorthodoxy prevailed at that time, Newton's friend William Whiston was deprived of his professorship and expelled from Cambridge University in 1710 for some of his imprudent remarks
2 Unfinished work, much less work done incorrectly is work the result of which cannot be used. After all, no one will go to work in a suit to which buttons are not sewn and does not drink coffee, in which salt was put instead of sugar.
