Abstract
This theoretical investigation develops analytical concepts on how to realize magnetic fields for the Multi to Mega Tesla realm within the range from milli to nano volumes and periods. The fields are anticipated to be realized using solenoids with multi-walled carbon (MWCNT) nanostructure composite metal windings. The study presented here opens up the issue of the miniaturization of large magnetic field systems. Concern has been raised that for such large magnetic fields and associated energies that the solenoidal structure may be highly reconfigured. Consequently, an investigation is undertaken of the tensile strength resulting from the azimuthal current. Also, the azimuthal power per turn will be addressed along with its limitations in generating the magnetic field. Further, the study finds the allowable eigenvalue frequencies of the electric field. Tables are provided for given values of Bz0(0) from 2T to 2(10)6T for a number of important parameters for consideration in designing solenoidal systems.
Highlights
Introduction to LinearAnalysis” byKreider, et al., p620, evaluating ˆH ˆE π Bz20 (0) 2μ0 (29) ExamplesThe two examples to follow are for the cases of the first order field eigenvalue mode, and the fourth order field eigenvalue mode
The potential parameters for assessing the theory presented for large magnetic field solenoidal systems with for example, multi-walled carbon nanotube (MWCNT) – copper composite windings, Subramanian, et al.[1], include the magnetic fields of Bz0(0) ranging in multiples of 10 from 2T to 2(10)6T
When considering prototypes for the first eigenvalue mode, the potential parameters to aid in accessing the theory are presented in Table 1 for large magnetic field solenoidal systems with MWCNT-copper composite windings
Summary
The vectors used in the analysis are defined as:. B = the magnetic field density vector, H = the magnetic field intensity vector, E = the electric field intensity vector, D = the electric field intensity vector j = the electric current surface density, ρ = volume electric charge density, where B = μ H and D = ε E and the physical constants being μ = the magnetic permeability, ε = the electric permittivity. The perfect conductor assumption approximation is based upon first noting the values measured by Subramanian, et al.[1] for their carbon-copper nanotubes are jθ = 6(10)12A/m2 and the conductivity σ = 4.7(10)[7] s/m By using these values, from Ohm’s Law, the electric field in the windings of the coil enclosing the solenoid is 1.3 (10)[5] V/m. The above evaluation gives a radial distance that is 99% of the eigenvalue distance at the coil From this information the perfect conductor assumption approximation appears appropriate for the analysis given since over 99% of the radial distance the effect of the electric field in the windings of the coil is negligible for the study.
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