Diffusive time evolution of the Grad–Shafranov equation for a toroidal plasma

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
Giovanni Montani ◽  
Matteo Del Prete ◽  
Nakia Carlevaro ◽  
Francesco Cianfrani
Keyword(s):  
Time Scale ◽  
Diffusion Time ◽  
Test Facility ◽  
Plasma Equilibrium ◽  
Toroidal Plasma ◽  
Divertor Tokamak ◽  
Analytical Properties ◽  
Shafranov Equation ◽  
Consistent Solution ◽  
Diffusive Time

We describe the evolution of a plasma equilibrium having a toroidal topology in the presence of constant electric resistivity. After outlining the main analytical properties of the solution, we illustrate its physical implications by reproducing the essential features of a scenario for the upcoming Italian experiment Divertor Tokamak Test Facility, with a good degree of accuracy. Although we find the resistive diffusion time scale to be of the order of $10^4$ s, we observe a macroscopic change in the plasma volume on a time scale of $10^2$ s, comparable to the foreseen duration of the plasma discharge by design. In the final part of the work, we compare our self-consistent solution to the more common Solov'ev one, and to a family of nonlinear configurations.

Bound for the pressure integral in a toroidal-plasma equilibrium

1993 ◽  
Vol 48 (3) ◽  
pp. 2133-2135
Author(s):  
Zensho Yoshida ◽  
Yoshikazu Giga
Keyword(s):  
Plasma Equilibrium ◽  
Toroidal Plasma

scholarly journals Modes of Operation of Thermo-Mechanically Coupled Ice Sheets

1989 ◽  
Vol 12 ◽  
pp. 57-69 ◽  
Author(s):  
Richard C.A. Hindmarsh ◽  
Geoffrey S. Boulton ◽  
Kolumban Hutter
Keyword(s):  
Temperature Field ◽  
Time Scale ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Thermal Inertia ◽  
Coupled System ◽  
Thermal Processes ◽  
Temperature Dependent ◽  
Geothermal Heat ◽  
Diffusive Time

A dimensionless model of thermo-mechanically coupled ice sheets is used to analyse the operation of the system. Three thermal processes are identified: (i) dissipation, having a maximum time-scale of thousands of years; (ii) advection, having a time-scale of tens of thousands of years; and (iii) conduction, having a time-scale of 100000 years. Kinematical processes occur on two time-scales: (i) a marginal advective time-scale of thousands of years; and (ii) a diffusive time-scale of tens of thousands of years dominant in the divide area.The coupling with the temperature field in the bed produces fluctuations to the depth of a few kilometres, which means that horizontal conduction in the bed can be ignored except perhaps in the marginal area. The thermal inertia of the bed could produce significant fluctuations in the geothermal heat gradient.The operation of the thermo-mechanically coupled system is explored with a time-dependent thermo-mechanically coupled numerical algorithm. Dependence of the basal friction on temperature is introduced heuristically, and an enthalpy method is used to represent the effect of latent heat. The marginal area is shown to be dissipation-driven, and always reaches melting point. The divide area can show two modes of behaviour: a warm-based mode where the ice sheet is thin, and a cold-based mode where the ice sheet is thick. Which mode operates depends upon the applied temperature field and the amount of heat conducted from the bed.Calculations where sliding is limited were not found to be possible owing to problems with the reduced model which resulted in a violation of the approximation conditions at the margin. Cases which did work required a substantial sliding component; as a result, a significant coupling between geometry and temperature can only be demonstrated when sliding is made temperature-dependent.

Estimation of formation temperature from bottom‐hole temperature measurements: COST ♯1 well, Norton Sound, Alaska

Geophysics ◽  
1988 ◽  
Vol 53 (12) ◽  
pp. 1619-1621 ◽  
Author(s):  
S. Cao ◽  
C. Hermanrud ◽  
I. Lerche
Keyword(s):  
Thermal Conductivity ◽  
Numerical Method ◽  
Time Scale ◽  
Efficiency Factor ◽  
Diffusion Time ◽  
Formation Temperature ◽  
Temperature Estimation ◽  
Bottom Hole ◽  
Free Parameters ◽  
Borehole Temperature

We recently developed a numerical method, the Formation Temperature Estimation (FTE) model, to determine formation temperatures by inversion of borehole temperature (BHT) measurements (Cao et al., 1988a). For more than two BHT measurements, the FTE model can estimate (1) true formation temperature [Formula: see text], (2) mud temperature [Formula: see text] at the time the mud circulation stops, (3) thermal invasion distance R into the formation before the formation is at the true formation temperature, (4) formation thermal conductivity K perpendicular to the borehole, and (5) efficiency factor F for mud heating in the borehole after mud circulation has stopped. The method optimizes three free parameters: τ (diffusion time‐scale), ε (scaling parameter related to the thermal invasion distance R), and [Formula: see text] (normalized efficiency factor for mud heating.

Interface and requirements management for the Divertor Tokamak Test facility

2019 ◽  
Author(s):  
Giovanni Tenaglia ◽  
Francesco Romanelli ◽  
Stefano La Rovere ◽  
Gian Mario Polli ◽  
Giuseppe Ramogida
Keyword(s):  
Test Facility ◽  
Requirements Management ◽  
Divertor Tokamak

Effect of plasma flow on the equilibrium of an axisymmetric toroidal magnetic trap

1997 ◽  
Vol 58 (3) ◽  
pp. 421-432 ◽  
Author(s):  
ZH. N. ANDRUSHCHENKO ◽  
O. K. CHEREMNYKH ◽  
J. W. EDENSTRASSER
Keyword(s):  
Plasma Flow ◽  
Magnetic Trap ◽  
Plasma Equilibrium ◽  
Plasma Rotation ◽  
Stationary Plasma ◽  
Shafranov Equation ◽  
Nonlinear Vector ◽  
Analytical Expressions ◽  
Poloidal Rotation ◽  
Shafranov Shift

The effect of finite plasma rotation on the equilibrium of an axisymmetric toroidal magnetic trap is investigated. The nonlinear vector equations describing the equilibrium of a highly conducting, current-carrying plasma are reduced to a set of scalar partial differential equations. Based on Shafranov's well-known tokamak model, this set of equations is employed for the description of a kinetic (stationary) plasma equilibrium. Analytical expressions for the Shafranov shift Δ are found for the case of finite plasma rotation, where two regions of possible plasma equilibria are found corresponding to sub- and super-Alfvénic poloidal rotation. The shift Δ itself, however, turns out to depend essentially on the toroidal rotation only. It is shown that in the case of a stationary plasma flow, the solution of the Grad–Shafranov equation is at the same time also the solution of the stationary Strauss equation.

Status of Internal-Tin Nb3Sn Strand for Divertor Tokamak Test Facility

2020 ◽  
Vol 30 (4) ◽  
pp. 1-4
Author(s):  
Jianwei Liu ◽  
Yigong Shi ◽  
Bo Wu ◽  
Ke Zhang ◽  
Sheng Liu ◽  
...  
Keyword(s):  
Test Facility ◽  
Divertor Tokamak ◽  
Nb3sn Strand
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