1. Introduction

Magnetic flux density tends to be pretty impressive. Fermi Walker systems are flexible connections of fluxes, solids, and streams, are full of relationship, model nonlinear equations, and are solidly influenced by magnetic variations. These quasi systems are more generous, enveloping biomaterials, liquids, polymers, gels, and foams, and have an extensive range of associated uniformly motions. Proceeding with these motions desires a hidden characterization of complexities of these profuse Magnetic flux systems [¹].

A great hypersensitive magnetic torque calibrates for operation in fluctuated large electromagnetic fields has been importuned, exclusively for direction of formulation scientific electromagnetic densities of original magnetic particles. Thus, densities are of powerful influence from perspective of perception of peculiar magnetic attributes. Also, even with last advancement of crystal magnetic theory, it is not uncomplicated to expand magnetic crystals by magnetic moments.

Uniformly accelerated structures have been obtained in [²] and, more recently, in Refs. [³,⁴]. In this paper, authors suggest new methods for finding solutions for uniformly quasi accelerated motion in a general curved spacetime. This extends results of [⁵], where explicit solutions are computed for flat spacetime only. Other approaches rely on convenient use of Frenet equations [⁶,⁷].

Magnetic flux density combinations are extensively operated as a magnetic moment component considering numerous varieties of machines like potential generators, turbines and activators. Magnetic hybrids are frequently embittered with meanwhile application of these machines. Melting is a result of the destruction of electrical energy at the elastic magnetic torque. Accordingly, advancement in the capability of elastic magnetic torque is momentous to recover the electrical energy and to bypass to contaminate bordering machines. Hence, preserving electrical energy benefits at preserving the earth’s ordinary reserves and climates. The inferior amorphous-forming capability of hybrids combines cripples with its operational capability at power generators and turbines [⁸].

Electromagnetic cover, just as an appropriate cover approach to establish a point, has explicit operation forecasts in various areas, being biomedicine, essential sensibility, and act cover [⁹]. The ultimate significant utilization areas are essentially nosy surgery [¹⁰]. The electromagnetic cover system may be managed like a split of the navigation structure to establish a certain-future situation for the pharmaceutical apparatus in the inmate’s frame, implement extreme advantage to scientists [¹¹]. Correlated with alternative navigation designs as optical new navigation, the electromagnetic cover has no radioactivity cripple or no constraint of radiation procedure. Also, an electromagnetic traverse system found on abstain energy of some magnetic flux density field characterized by some azimuth intersection is recommended [¹²].

The biharmonic particles also play an important role in geometry. Also, a large number of experts have analyzed geometric biharmonic particles and surface conditions, [¹³,¹⁴]. On the other hand, the energy concept has been obtained with some characterizations, [¹⁵-¹⁹].

Magnetic particles provide an impressive, reliable, and densely parallel synthesized attitude. By utilizing magnetic torque, principal magnetic matter experimenters have established advanced technologies in physics, optics, world sciences, and basic materials. Categorically, magnetic torque has been managed to construct particle interruptions, to assemble an influence fusion magnetic particles, and to apply and shape optical materials [²⁰-²⁵].

Aim of the research work, a general construction method is proposed for magnetic interpretation of new quasi uniformly accelerated potential electric energy and Fermi parallel transportation in cold plasma with illustrations of results. We consider the quasi uniformly accelerated motion with some Lorentz fields. The applications of these models are geometric and physical interpretations of quasi uniformly accelerated potential electric energy.

The construction of our article is as follows: Firstly, we construct the quasi uniformly accelerated motion (QUAM) with Fermi derivative by cold plasma in Heisenberg space. We define new quasi uniformly accelerated potential electric energy of quasi normal magnetic biharmonic particles and some Lorentz fields. Moreover, we design the new relationship between the quasi uniformly accelerated motion and the Fermi parallel transportation in cold plasma. Also, we collect new physical geometric designs for a quasi uniformly accelerated motion of normal magnetic biharmonic particles in Heisenberg space. Finally, we construct quasi uniformly accelerated potential electric energy with respect to its electric field and some quasi curvatures.

2. Backround on quasi frame and Heisenberg space

Heisenberg space have following metric [²⁶]:

Heisenberg space’s basis is given by

Let α be a particle with arclength. Also, t, n, and b describe tangent, principal normal, and secondary normal fields, respectively. Then, Frenet equations are given by

where κ and τ are curvatures of particles.

A new quasi frame of a particle is presented by [²⁷],

where k= (0,0,1) is the projection field.

Since the new quasi frame is provided by

where the angle ψ is between the quasi field n _q and the vector n and

3. Quasi uniformly accelerated motion of quasi normal magnetic biharmonic particles

In this section, we characterize the quasi uniformly accelerated motion of moving charged quasi normal magnetic biharmonic particles with unit speed normal magnetic biharmonic particles in Heisenberg space. We obtain necessary and sufficient conditions that have to be satisfied by the particle in terms of the Frenet scalars of the worldline of magnetic curves. We present the following definition of the quasi uniformly accelerated motion.

Let α be a biharmonic particle and B be a magnetic field in the Heisenberg space. We call the curve α as a quasi normal magnetic biharmonic particle if the quasi normal field of the biharmonic particle meets the following Lorentz force equation.

Fermi Walker derivative of any field R is defined by

where ∇ is Levi-Civita connection associated metric h [²⁸].

♣ The particle X is quasi uniformly accelerated motion iff

• Lorentz force of T _q , N _q , B _q are presented

where ω = φ(T _q) · B _q .

• Magnetic vector field B of normal magnetic biharmonic particle is given by

Lemma 1.

♣ Fermi Walker derivative of φ(T _q) is

♣ Fermi Walker derivative of φ(N _q) is

♣ Fermi Walker derivative of φ(B _q) is

♣ Fermi Walker derivative of B is

Lemma 2.

♣ φ(T _q) is Fermi Walker parallel iff

♣ φ(N _q) is Fermi Walker parallel iff

♣ φ(B _q) is Fermi Walker parallel iff

♣ B is Fermi Walker parallel iff