Probable reasons are discussed why the absorbed energy determined from diamagnetic measurements in experiments on electron cyclotron resonance plasma heating is less than the input microwave energy.
Various methods of determining the ambipolar electric field in toroidal magnetic systems (predominantly, in stellarators) and the evolution of views on this problem are discussed. Paradoxes ...encountered in solving this problem are analyzed, and ways of resolving them are proposed.
Backscattering of gyrotron radiation (θ = π) by short-wavelength density fluctuations (
k
⊥
= 30 cm
−1
) in the plasma of the L-2M stellarator was studied under conditions of electron cyclotron ...resonance (ECR) plasma heating at the second harmonic of the electron gyrofrequency (75 GHz). The scattering of the O-wave emerging due to the splitting of the linearly polarized gyrotron radiation into the X- and O-waves was analyzed. The signal obtained after homodyne detection of scattered radiation is a result of interference of the reference signal, the quasi-steady component, and the fast oscillating component. The coefficients of reflection of the quasi-steady component,
R
=
2
(
Y
), and fast oscillating component,
R
∼
2
(
Y
), of scattered radiation are estimated. The growth of the
R
∼
2
(
Y
) coefficient from 3.7 × 10
−4
to 5.2 × 10
−4
with increasing ECR heating power from 190 to 430 kW is found to correlate with the decrease in the energy lifetime from 1.9 to 1.46 ms. The relative density of short-wavelength fluctuations is estimated to be 〈
n
∼
2
〉/〈
n
e
2
〉 = 3 × 10
−7
. It is shown that the frequencies of short-wavelength fluctuations are in the range 10–150 kHz. The recorded short-wavelength fluctuations can be interpreted as structural turbulence, the energy of which comprises ∼10% of the total fluctuations energy. Simulations of transport processes show that neoclassical heat fluxes are much smaller than anomalous ones. It is suggested that short-wavelength turbulence plays a decisive role in the anomalous heat transport.
In order to model transport processes in magnetic confinement systems, it is necessary to have information on the charged particle source. This in turn requires calculation of the inward flux of ...neutral particles. In this paper, a method for solving this problem in the hydrodynamic approach for the neutral gas is proposed. The average velocity of neutral particles and the spatial distribution of their density are determined. The obtained expression for the neutral density almost completely coincides with that calculated previously by solving the kinetic equation. However, the computational time required to solve the problem in the proposed hydrodynamic approach is much shorter than that in the kinetic approach.
It was shown earlier that, in the range of rare collisions, transport equations for stellarators allow steady discontinuous solutions for the ambipolar electric field and for the plasma density and ...temperature gradients. Moreover, such solutions are non-single-valued; that is, their explicit form depends on the initial values of the ambipolar electric field. The time-independent transport equations are derived under the conventional quasineutrality condition; i.e., it is assumed that the electron and ion densities,
N
e
and
N
i
, are related by the relationship
N
e
=
ZN
i
(where
Z
is the ion charge number). In other words, the plasma charge density is assumed to be much less than the product
e
i
N
i
. Under typical conditions, the corresponding inequality is satisfied by a large margin. However, if the electric field
E
has discontinuities, then it can be seen from the equation ▿·E = 4πρ that, at the discontinuity points, the charge density becomes infinite and the relationship
N
e
=
ZN
i
fails to hold, so it is necessary to replace it with
N
e
=
ZN
i
+ ρ/
e
e
. In the transport equations, this latter replacement produces additional terms, proportional to the second radial derivative of the field
E
. With these additional terms, the steady solutions are modified substantially. First, the ambipolar field and the derivatives of the density and temperatures all become continuous functions of the coordinates, a result that seems to be quite obvious. The second, not-so-obvious result is that the steady solutions become single-valued, i.e., independent of the initial values of the ambipolar electric field. It turns out that, in this case, two regimes are possible, depending on the values of the plasma parameters. In the first regime, the solution is unique and is independent of the initial conditions. In the second regime, two steady solutions can exist, depending on the initial conditions. One of the solution is similar to that obtained in the first regime, and the other differs from the first one both in the ambipolar field profile and in the dependence of the density and temperatures on the minor plasma radius. It cannot be excluded that different plasma confinement modes revealed in experiments are associated with the existence of such solutions.
A relatively simple model of transport process in stellarators that was proposed earlier by the author on the basis of neoclassical theory makes it possible to determine the density and temperature ...profiles of the plasma components, the ambipolar electric field profile, and the particle and energy lifetimes from the given device parameters and given particle and energy sources with allowance for anomalous losses. The results of numerical simulations carried out with this model for the L-2M, ATF, CHS, and LHD stellarators over broad ranges of plasma densities and absorbed powers showed that the plasma energy lifetimes in these devices coincide to within factors on the order of two with those found from empirical scalings. A specific model of anomalous losses was chosen for calculations. Results are presented from simulations with a more general form of the anomalous thermal conductivity. Namely, the thermal conductivity is chosen to be
K
j
(
a
)
≈
N
α
T
j
β
B
0
−γ
, where
N
(
r
) is the plasma density and
T
j
(
r
) is the temperature of the
j
th plasma component (
j
=
e, i
). The parameters α, β, and γ are set equal to α = 1, β = 2, and γ = 1; α = 0.5, β = 2.5, and γ = 1; α = 1.5, β = 2, and γ = 2; α = 1, β = 2.5, and γ = 2; and α = 1.5, β = 2.5, and γ = 2. The simulations have been done for the L-2M and LHD stellarators. It is found that, in all the five models, the calculated energy lifetimes τ
c
are essentially independent of the functional form of the anomalous thermal conductivity and coincide to within a factor on the order of two with those following from the LHD scaling.
The question of whether two-valued solutions can exist for an ambipolar electric field in stellarators and rippled tokamaks is considered. Steady solutions to transport equations in the limit of ...infrequent collisions are obtained in the purely neoclassical transport theory (that is, without allowance for possible anomalous losses). It is shown that, given the particle and heat sources, these equations have only one steady continuous solution, i.e., the steady states are nonbifurcating.
The possibility of steady-state multivalued solutions to transport equations in stellarators is considered. It is shown that the ambipolarity condition is necessary but not sufficient to find the ...ambipolar electric field, because the functions entering into it (the plasma density and temperature, as well as their spatial derivatives) depend on the ambipolar field. To do this correctly, it is necessary to solve the full set of time-independent transport equations (including diffusion and heat conduction equations). The possible existence of multivalued solutions to this set of equations is analyzed numerically. It is shown that, under certain conditions that depend on the form and magnitude of particle and heat sources, such solutions can exist. Their form is determined by the initial value of the ambipolar field, the source magnitudes, and the boundary conditions. Discontinuous solutions in which the radial profile of the ambipolar field undergoes jumps are found. In this case, however, the particle and energy fluxes remain continuous, because the discontinuities of the electric field are balanced by the discontinuities of the density and temperature gradients.
