VERSATOR II and PLT plasmas

E.2 VERSATOR II and PLT plasmas

E.2.1 Equilibrium

Figure 7: Poloidal projection of the ray trajectory. The red curve corresponds to the slow mode and the blue curve corresponds to the fast mode. Numeric (upper plot) and analytic (lower plot) magnetic equilibrium. VERSATOR II. N_∥0 = 5.0.

Figure 8: Poloidal projection of the ray trajectory. The red curve corresponds to the slow mode and the blue curve corresponds to the fast mode. Numeric (upper plot) and analytic (lower plot) magnetic equilibrium. PLT, N_∥0 = 1.33.

Figure 9: Radial position of the ray trajectory as function of the toroidal angle (PLT). N_∥ = 1.33.

Figure 10: Poloidal position of the ray trajectory as function of the toroidal angle (PLT). N_∥ = 1.33.

Figure 11: Parallel refractive index or refraction along the ray trajectory as function of the toroidal angle (PLT). N_∥ = 1.33.

Figure 12: Perpendicular refractive index or refraction along the ray trajectory as function of the toroidal angle (PLT). N_∥ = 1.33.

Lower Hybrid heating and current drive simulations have been performed for the VERSATOR II and PLT tokamaks, which both have almost circular concentric magnetic flux surfaces [1, 10]. For the sake of benchmarking, the Shafranov shift is neglected, and a plasma with exact circular concentric magnetic flux surfaces is considered with the following magnetic equilibrium parameters

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(172)

and the following profiles

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(173)

with

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(174)

In the calculations, the scrape-off layer is not considered, since the specular reflection is enforced if needed on the last closed magnetic surface for the Lower Hybrid wave.

For both tokamaks, Z_eff is uniform with Z_eff = 4 for VERSATOR II and Z_eff = 2 for PLT. The plasma is made of hydrogen ions for VERSATOR II and deuterium ions for PLT. For both machines, a fully stripped single impurity species is considered, using carbon ions with m_c = 12, Z_c = 6.

The magnetic equilibrium is characterized by a parabolic safety factor profile

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(175)

The poloidal flux coordinate ψ is then

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(176)

which leads to

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(177)

In the simulations, q_min = 1, and q_max is obtained from Ampère’s law.

E.2.2 Wave initial conditions

For both tokamaks, the ray is launched in the slow mode from the position

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(178)

with the spectral properties

\text{[math]}

(179)

The non-zero m₀ arises from the fact that simulations in references [1] [10] use m₀ = 0 in the scrape-off layer and not at ψ = ψ_a.

E.2.3 Results

The results are plotted in figures 7-12. A good agreement is found with references [1] and [10] despite differences in the magnetic equilibrium. An excellent agreement is found between numerical and analytical magnetic equilibrium for the case of VERSATOR II where the ray never approaches the plasma center.

The difference arises from a cumulative error that becomes more important when the ray approaches the plasma center. Yet the effect on the wave power and current deposition generally remains negligible.

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