Analytical analysis of the generation of a rotating driving magnetic field on the outer surface of a magnetic pinch load with a helical return current post

A recently emerging approach adopts a directionally time-varying (rotating) magnetic field to drive a pinch load, aiming to mitigate the inherent magneto-Rayleigh-Taylor instability in dynamic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>Z</a:mi></a:mrow></a:math> pinches. A helical return current post (RCP) serves as a functional structural element capable of generating the requisite driving magnetic field for this purpose in the load region. This paper first calculates the current azimuthally induced on the outer surface of a magnetically pinched load within this type of RCP using a zero-dimensional lumped-parameter circuit model. The results show that the induced current deviates significantly from the presumed “perfect” induced current (100% amplitude) as reported in the literature [S. A. Sorokin, ); P. F. Schmit , ); G. A. Shipley , ); and P. C. Campbell , ], with an effective coefficient of current induction considerably less than 1. However, even when the load is fully compressed to the axis, the effective coefficient does not approach zero but rather converges to a finite value that solely depends on the aspect ratio of the RCP. This is quite favorable for the suppression of magneto-Rayleigh-Taylor instability in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>Z</c:mi></c:mrow></c:math> pinch. As for the pointlike <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>X</e:mi></e:mrow></e:math> pinch, the axial magnetic field does not tend to zero but a finite value, though the effective coefficient tends to zero, and this result may be used to suppress the instability in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>X</g:mi></g:mrow></g:math> pinch and improve the time stability and spatiotemporal unity of hot spots. In addition, the anode and cathode plates have the potential to enhance the current induced in the load. This paper then analyzes the axial distribution and time behavior of the induced current adopting an approximate analytical method and numerical integration and finds an approximate invariance that can be well characterized by <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>δ</i:mi><i:mi>t</i:mi></i:mrow></i:math>, the product of the normalized skin depth and time. Similar values of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mi>δ</k:mi><k:mi>t</k:mi></k:mrow></k:math> indicate similar axial distribution characteristics. When <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mi>δ</m:mi><m:mi>t</m:mi></m:mrow></m:math> is lower than, at, or higher than the critical region (<o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:mo form="prefix">∼</o:mo><o:mn>0.1</o:mn><o:mi>–</o:mi><o:mn>0.3</o:mn></o:mrow></o:math>), the axial distribution appears dumbbell shaped, nearly flat, and arched, respectively. These distributively induced currents can be exploited to achieve quasispherical, near flat, and dumbbell-shaped implosions, respectively.