Units and symbols. 1 Fusion. Fusion and tokamaks Fusion reactions Thermonuclear fusion Power balance Ignition. Large aspect-ratio. Shafranov shift. Tokamak plasma. Vacuum magnetic field. Debye shielding. Electric fields. 1. Electromagnetism. Fluid equations. 1,1. Fusion and tokamaks. 2. Magnetohydrodynamics. Fusion reactions. 3. 2, Physics.

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Relevant Polywell Material. Contribute to ThePolywellGuy/Polywell-Papers development by creating an account on GitHub. Request PDF on ResearchGate | On Sep 1, , John I. B. Wilson and others published Tokamaks, 4th edn., by John Wesson. Reader; beware of the subtitle! The main title of this volume proclaims an interesting and worthwhile goal. A thorough knowledge of cosmic rays would surely be.

Abdullaev Drifts of electron orbits induced by toroidal electric field in tokamaks S. Abdullaev Citation: Physics of Plasmas present 22, ; doi: Plasmas 19, ; Plasmas 18, ; Plasmas 16, ; Plasmas 13, ; Plasmas 12, ;

With the further increase of the RE energy, the orbit crosses the separatrix a homoclinic orbit associated the X-point and hits the wall. Equation 15 describes not only the outward drift of passing particles but also the inward drift of trapped particles known as the Ware pinch7 see, also Ref. Curve 1 corresponds to vdr Ri , curve 2—to vdr Ro , and It is important to note that the drift of the electron GC curve 3 the right hand axis describes the adiabatic invariant J t normalized to its initial value J 0.

Figure 2 illustrates the evolution of an The drift velocity vdr is proportional to the strength of initially trapped electron orbit into a passing one: at a certain the toroidal electric field Eu and to the inverse of the plasma time, due to its inward drift, the banana orbit turns into a FIG. The plasma parameters are the same as in Fig. This article is copyrighted as indicated in the article. We should note that the formation of the separatrix of the GC orbit in the toroidal electric field has first been pre- dicted three decades ago in Ref.

This phenomenon has been only recently confirmed by numerical simulations in re- alistic tokamak conditions during plasma disruptions.

This factor is only weekly sensitive to the toroidal magnetic field B0 and plasma current Ip.

Numerical calculations the electron energy. Therefore, one expects the outward drift velocity point of a GC orbit shown by curve 2 in Fig. It describes the outward drift of passing electrons of the electron energy E and at the critical value Ecr, the field as well as the inward drift of trapped electrons.

The critical energy Ecr for the creation of the X-point can be 1 J. Wesson, Tokamaks, 3rd ed. Clarendon Press, Oxford, Guan, H. Qin, and N. Fisch, Phys. Plasmas 17, For sufficiently large energy with the relativistic fac- 3 H.

Qin, X. Guan, and N. Neglecting the last term Laboratory, Report No. PPPL, Zehrfeld, G. Fussmann, and B. Green, Plasma Phys.

Wongrach, K. Finken, S.

Abdullaev, R. Our considerations are based on the Hamiltonian formu- For passing particles one can choose the toroidal angle lation of relativistic GC motion in a toroidal system see Ref. Abdullaev Phys. We assume axisymme- try, i. B0 R20 Expression 15 is obtained by expansion of 13 with Here w 0 x, z is the poloidal flux of the equilibrium plasma. That has been confirmed by numerical calculations.

Plasmas 22, current Ip, i.

For REs, the outermost point drifts faster than the innermost point, i. This leads to an elongation of the orbit along the radial direction.

In particular, an initially circular orbit evolves into an oval shaped one owing to the electron acceleration. Figures 1 a and 1 b illustrate the evolution of the GC orbit and the out- ward drift velocities vdf Ri , vdf Ro in a tokamak plasma. With the further increase of the RE energy, the orbit crosses the separatrix a homoclinic orbit associated the X-point and hits the wall.

Equation 15 describes not only the outward drift of passing particles but also the inward drift of trapped particles known as the Ware pinch7 see, also Ref. Curve 1 corresponds to vdr Ri , curve 2—to vdr Ro , and It is important to note that the drift of the electron GC curve 3 the right hand axis describes the adiabatic invariant J t normalized to its initial value J 0.

Figure 2 illustrates the evolution of an The drift velocity vdr is proportional to the strength of initially trapped electron orbit into a passing one: at a certain the toroidal electric field Eu and to the inverse of the plasma time, due to its inward drift, the banana orbit turns into a FIG.

The plasma parameters are the same as in Fig. This article is copyrighted as indicated in the article. We should note that the formation of the separatrix of the GC orbit in the toroidal electric field has first been pre- dicted three decades ago in Ref. This phenomenon has been only recently confirmed by numerical simulations in re- alistic tokamak conditions during plasma disruptions. This factor is only weekly sensitive to the toroidal magnetic field B0 and plasma current Ip.

Numerical calculations the electron energy.

Therefore, one expects the outward drift velocity point of a GC orbit shown by curve 2 in Fig. It describes the outward drift of passing electrons of the electron energy E and at the critical value Ecr, the field as well as the inward drift of trapped electrons. The critical energy Ecr for the creation of the X-point can be 1 J.

Wesson, Tokamaks, 3rd ed. Clarendon Press, Oxford, Guan, H. Qin, and N. Fisch, Phys. Plasmas 17, For sufficiently large energy with the relativistic fac- 3 H.

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