THEORETICAL MODEL FOR A FINITE-THICKNESS GAS-PUFF Z-Θ PINCH

1993 ◽  
Vol 07 (26) ◽  
pp. 1655-1660 ◽  
Author(s):  
ARSHAD M. MIRZA ◽  
M. IQBAL ◽  
N.A.D. KHATTAK ◽  
G. MURTAZA
Keyword(s):  
Magnetic Field ◽  
Theoretical Model ◽  
Time Scale ◽  
Rise Time ◽  
Finite Thickness ◽  
Current Sheath ◽  
Constant Mass ◽  
Pinch Current ◽  
Z Pinch ◽  
Ultrahigh Magnetic Field

A dynamic model for a finite-thickness gas-puff Z-θ pinch is proposed. The snowplow effect is incorporated to describe the dynamics of an imploding annular plasma shell of finite thickness. Our numerical results demonstrate that for a thick gas-puff layer, fast compression occurs which produces an ultrahigh magnetic field on a time scale much less than the rise time of the Z-pinch current. For a very thin puff layer, however, the current sheath moves like a constant mass layer as described by Rahman et al.

Fusion conditions in a finite-thickness gas-puff staged Z-pinch

1994 ◽  
Vol 52 (3) ◽  
pp. 365-371 ◽  
Author(s):  
Arshad M. Mirza ◽  
N. A. D. Khattak ◽  
M. Iqbal ◽  
G. Murtaza
Keyword(s):  
Magnetic Field ◽  
Time Scale ◽  
Rise Time ◽  
Axial Magnetic Field ◽  
Finite Thickness ◽  
Order Of Magnitude ◽  
Stabilization Effect ◽  
Pinch Current ◽  
Short Time ◽  
Z Pinch

We investigate the implosion of a dense τ-pinch plasma driven by an annular finite-thickness gas-puff Z-pinch. The imploding Z-pinch traps an axial magnetic field Bz, compressing it to large values in an extremely short time. The temporal variation of Bz then induces an azimuthal τ current on the surface of a fibre placed on the axis, with a rise time an order of magnitude shorter than the rise time of the Z-pinch current. Our numerical results demonstrate that, for a thick gas-puff layer, maximum compression occurs before the current peaks.We also find that at peak compression, fuel densities of the order of 1025 cm-3 and temperatures above 10 keV can be achieved on a time scale of the order of 0.1 ns. Thus a Lawson parameter nτ ≈ 1014 s cm-3 for a DT fibre becomes achievable. The snowplough effect in the Z-pinch exercises a stabilization effect on the growth of sausage and Rayleigh—Taylor instabilities. In the limit of a very thin gas-puff layer, previous results are fully recovered.

scholarly journals Flux expulsion with dynamics

2016 ◽  
Vol 791 ◽  
pp. 568-588 ◽  
Author(s):  
Andrew D. Gilbert ◽  
Joanne Mason ◽  
Steven M. Tobias
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Lorentz Force ◽  
Differential Rotation ◽  
Time Scale ◽  
Scaling Laws ◽  
Dynamical Regime ◽  
Kinematic Evolution ◽  
Flux Expulsion ◽  
The Magnetic Field

In the process of flux expulsion, a magnetic field is expelled from a region of closed streamlines on a $TR_{m}^{1/3}$ time scale, for magnetic Reynolds number $R_{m}\gg 1$ ($T$ being the turnover time of the flow). This classic result applies in the kinematic regime where the flow field is specified independently of the magnetic field. A weak magnetic ‘core’ is left at the centre of a closed region of streamlines, and this decays exponentially on the $TR_{m}^{1/2}$ time scale. The present paper extends these results to the dynamical regime, where there is competition between the process of flux expulsion and the Lorentz force, which suppresses the differential rotation. This competition is studied using a quasi-linear model in which the flow is constrained to be axisymmetric. The magnetic Prandtl number $R_{m}/R_{e}$ is taken to be small, with $R_{m}$ large, and a range of initial field strengths $b_{0}$ is considered. Two scaling laws are proposed and confirmed numerically. For initial magnetic fields below the threshold $b_{core}=O(UR_{m}^{-1/3})$, flux expulsion operates despite the Lorentz force, cutting through field lines to result in the formation of a central core of magnetic field. Here $U$ is a velocity scale of the flow and magnetic fields are measured in Alfvén units. For larger initial fields the Lorentz force is dominant and the flow creates Alfvén waves that propagate away. The second threshold is $b_{dynam}=O(UR_{m}^{-3/4})$, below which the field follows the kinematic evolution and decays rapidly. Between these two thresholds the magnetic field is strong enough to suppress differential rotation, leaving a magnetically controlled core spinning in solid body motion, which then decays slowly on a time scale of order $TR_{m}$.

On Ultrahigh Magnetic-Field Generation Using Solid-State Liner System

2010 ◽  
Vol 38 (8) ◽  
pp. 1719-1722 ◽  
Author(s):  
Victor D Selemir ◽  
Vasily A Demidov ◽  
Pavel B Repin ◽  
Andrey P Orlov ◽  
Nikolay V Egorov
Keyword(s):  
Magnetic Field ◽  
Solid State ◽  
Magnetic Field Generation ◽  
Field Generation ◽  
Liner System ◽  
Ultrahigh Magnetic Field

Threshold for efferent bladder nerve firing in the rat

1999 ◽  
Vol 276 (6) ◽  
pp. R1819-R1824
Author(s):  
Els van Asselt ◽  
Joost le Feber ◽  
Ron van Mastrigt
Keyword(s):  
Theoretical Model ◽  
Rise Time ◽  
Afferent Nerve ◽  
Bladder Pressure ◽  
Afferent Activity ◽  
Nerve Activity ◽  
Efferent Activity ◽  
Rat Bladder ◽  
Bladder Contraction

In this study, the mechanism involved in the initiation of voiding was investigated. Bladder pressure and bladder and urethral nerve activity were recorded in the anesthetized rat. Bladder nerve activity was resolved into afferent and efferent activity by means of a theoretical model. The beginning of an active bladder contraction was defined as the onset of bladder efferent firing at a certain time ( t 0). From t 0 onward, bladder efferent activity increased linearly during δ t seconds (rise time) to a maximum. The pressure at t 0 was 1.0 ± 0.4 kPa, the afferent nerve activity at t 0 was 2.0 ± 0.6 μV (53 ± 15% of maximum total nerve activity), and δ t was 11 ± 13 s. Between contractions the afferent activity at t 0 was never exceeded. Urethral afferent nerve activity started at bladder pressures of 2.1 ± 1.1 kPa. Therefore, we concluded that urethral afferent nerve activity does not play a role in the initiation of bladder contractions; voiding contractions presumably are initiated by bladder afferent nerve activity exceeding a certain threshold.

scholarly journals Rotation and Magnetic Field Effect on Surface Waves Propagation in an Elastic Layer Lying over a Generalized Thermoelastic Diffusive Half-Space with Imperfect Boundary

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
Kh. Lotfy ◽  
A. Gohaly
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Half Space ◽  
Attenuation Coefficient ◽  
Elastic Layer ◽  
Finite Thickness ◽  
Relaxation Times ◽  
Magnetic Field Effect ◽  
Plane Boundary ◽  
Special Cases

The aim of the present investigation is to study the effects of magnetic field, relaxation times, and rotation on the propagation of surface waves with imperfect boundary. The propagation between an isotropic elastic layer of finite thickness and a homogenous isotropic thermodiffusive elastic half-space with rotation in the context of Green-Lindsay (GL) model is studied. The secular equation for surface waves in compact form is derived after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness, and then deduced for normal stiffness, tangential stiffness and welded contact. The amplitudes of displacements, temperature, and concentration are computed analytically at the free plane boundary. Some special cases are illustrated and compared with previous results obtained by other authors. The effects of rotation, magnetic field, and relaxation times on the speed, attenuation coefficient, and the amplitudes of displacements, temperature, and concentration are displayed graphically.

Buckling of a Superconducting Ring in a Toroidal Magnetic Field

1979 ◽  
Vol 46 (1) ◽  
pp. 151-155 ◽  
Author(s):  
F. C. Moon
Keyword(s):  
Magnetic Field ◽  
Theoretical Model ◽  
Toroidal Magnetic Field ◽  
Magnetic Fusion ◽  
Poloidal Field ◽  
Superconducting Ring ◽  
Tokamak Reactors ◽  
Linear And Nonlinear ◽  
Mode A ◽  
Theory And Experiment

Experimental evidence and a theoretical model are presented for the magnetoelastic buckling of a rigid superconducting ring in a steady circumferential (toroidal)magnetic field. The theoretical model predicts a coupled translation and pitch displacement of the coil in the buckled mode. A discussion is given of both the linear and nonlinear magnetic perturbation forces. The experiments were conducted in liquid helium (4.2°K). The lowest natural frequency of the rigid coil on elastic springs was observed to decrease near the buckling current. Agreement between theory and experiment is fair. These results may have design implications for poloidal field coils in magnetic fusion Tokamak reactors.

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