Strong and Superstrong Pulsed Magnetic Fields Generation

German A. Shneerson, Mikhail I. Dolotenko, Sergey I. Krivosheev

• Publisher: De Gruyter
• Year: 2014
• eBook ISBN: 9783110385182
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Strong pulsed magnetic fields are important for several fields in physics and engineering, such as power generation and accelerator facilities. Basic aspects of the generation of strong and superstrong pulsed magnetic fields technique are given, including the physics and hydrodynamics of the conductors interacting with the field as well as an account of the significant progress in generation of strong magnetic fields using the magnetic accumulation technique. Results of computer simulations as well as a survey of available field technology are completing the volume.

1 Magnetic fields of axially symmetrical magnetic systems used for generation of the strong fields (methods of calculation, assessment of the edge effects)

1.1 Magnetic field of the systems with the given current distribution

As a rule, the size of the pulsed devices-R_max do not exceed a few meters, and this is why at the characteristic frequencies of the order of 1 MHz and lower one can assume that discharge regimes are quasi stationary. This is valid if the case when

(λ is the electromagnetic wavelength in a vacuum) is not considered. Therefore the assumption on quasi stationary behavior is applied in all chapters of this book. The vector of induction in the space outside of conductors at these conditions obeys the Maxwell equations ^[1][2][3]:

(1.1)

(1.2)

In this chapter we consider the often exploited configurations of solenoid used at the generation of strong and superstrong fields. In the axis symmetrical configurations (Figure 1.1) two types of magnetic structures are possible: poloidal and azimuthal fields. In Table 1.1 we present the components of the vector potential and vectors of induction and current density for both of these field configurations.

At the given current distribution the induction of the toroidal field, having only one component could be calculated from the law of the total current:

(1.3)

where r is the radial coordinate of the point N, and

is the total current passing through the circle with radius r.

The azimuthal component of the vector potential A_ϕ, flow function

and the scalar magnetic potential U_M of the axialy symmetrical poloidal field satisfy to the following equations reduced from Maxwell equations:

(1.4)

(1.5)

(1.6)

Fig.1.1: Magnetic systems with the field depending on two coordinates: (a) axis symmetrical toroidal field with

; (b) axis symmetrical poloidal field with B = (B_r,, 0, B_z),

(c) flat analog to the toroidal field with B = (0, 0, B_z),

=

; (d) flat analog to the poloidal field with B = (B_x, B_y, 0),

.

Table 1.1: Two types of magnetic fields: poloidal and toroidal.

The vector of induction of poloidal field outside of conductor is expressed via the functions U_M, A_ϕ and Ψ by the well-known formulas

(1.7)

(1.8)

At known axially- symmetrical current distribution on the cross section of solenoid winding, the vector potential of the poloidal field in the arbitrary point N with cylindrical coordinates r, z is expressed in a following way:

(1.9)

where r_t, z_t, ϕ_t are the coordinates of the point t, on the cross section of the conductor r_t, z_t, ϕ_tr_t, T and K(k) and E(k) are complete elliptic integrals with module k = 2(rr_t)^1/2[(z−z_t)² + (r+ r_t)²]^−1/2.

From here one can obtain the expressions for the induction on the axis of the solenoid:

(1.10)

and the important formulas f...

Table of contents

• De Gruyter Studies in Mathematical Physics
• Title Page
• Copyright Page
• Table of Contents
• Introduction
• 1 Magnetic fields of axially symmetrical magnetic systems used for generation of the strong fields (methods of calculation, assessment of the edge effects)
• 2 Calculating formulas and the results of numerical estimations of field parameters for typical single-turn magnets
• 3 Field diffusion into the conductors and their heating
• 4 Matching of the parameters of solenoids and power supply sources
• 5 Electromagnetic forces and mechanical stresses in multiturn solenoids. The optimization of multilayered windings
• 6 Generation of strong magnetic fields in multiturn magnets
• 7 Solenoids with quasi-force-free windings
• 8 Generation of strong pulsed magnetic fields in single-turn magnets. Magnetic systems for the formation of pulsed loads
• 9 Generation of ultrahigh magnetic fields in destructive single-turn magnets
• 10 Magnetic cumulation
• Index