TEK benchmarking with GENE in DIII-D cyclone base case

7 TEK benchmarking with GENE in DIII-D cyclone base case

The DIII-D cyclone base case is a circular and concentric magnetic conﬁguration. The main parameters are summarized in Table 1. All parameters are the same as those in T. Gorler’s paper[4]. (This conﬁguratgion was inspired by DIII-D H-mode discharge #81499 and used in the cyclone project for benchmarking various gyrokinetic ITG turbulence simulations.)


R₀	a	r₀	q₀	ŝ₀	B_axis	_{T_i}R₀	_{n_i}R₀	T_i0	q_iT_i0∕(eT_e0)

1.67m	0.60m	0.30m	1.41	0.84	2.0T	6.96	2.23	2.14keV	1

Table 1: DIII-D cyclone base case parameters[2][4] where R₀ is the major radius of the magnetic axis, a is the minor radius of the last-closed-ﬂux-surface, q₀ is the value of safety factor at r = r₀ = 0.5a, ŝ₀ is the value of the magnetic shear ŝ = rq⁻¹dq∕dr at r = r₀. B_axis is the magnetic ﬁeld strength at the magnetic axis. The toroidal ﬁeld function g(r) = B_ϕR is assumed to be a constant independent of r, i.e., g = B_axisR₀. T_i0 is the ion temperature at r = r₀. Assume Deuterium plasma, then R₀∕ρ_i = 500 and a∕ρ_i = 180. where ρ_i = ∘ ------
Ti0∕mi

∕Ω_i is the thermal ion gyro-radius, Ω_i = B_axisq_i∕m_i is the ion cyclotron angular frequency at the magnetic axis.

The safety factor proﬁle is chosen as [6]

2 q(r) = 0.86− 0.16r∕a+ 2.52(r∕a)

This proﬁle gives q₀ ≡ q(0) = 1.41 and ŝ = 0.84 at r = r₀. The equilibrium ion temperature and number density proﬁle are given by

( (r − r0) ) Ti = Ti0exp − ˆκTiaΔTi tanh ----- . ΔTia

(283)

( ( )) r-−-r0 ni = ni0exp − ˆκniaΔni tanh Δnia .

(284)

where Δ_{T_i} = Δ_{n_i} = 0.3, n_i0 = 4.66 × 10¹⁹m⁻³, T_i0 = 2.14keV. Then the radial derivatives are written as

( ) dTi = T(− ˆκ aΔ )-d tanh r−-r0 dr i Ti Tidr ΔTia 2( r−-r0) --1-- = Ti(− ˆκTiaΔTi) sech ΔTia ΔTia ( r− r ) = − TiˆκTi sech2----0 ΔTia

The corresponding gradient scale lengths of T_i and n_i are then given by

( ) κTi = − 1-dTi = ˆκTi sech2 r−-r0 , Ti dr ΔTia

(285)

and

( ) 1-dni 2 r−-r0 κni = − ni dr = ˆκni sech Δnia ,

(286)

where sech²(⋅) ≡ 1 − tanh²(⋅). The electron density and temperature proﬁles are assumed to be identical to those of ions. The electron mass is set as m_e = 1.82 × 10⁻³⁰kg, i.e., two times the realistic value of electron mass.

The proﬁles of safety factor, temperature, and density are plotted in Fig. 3.

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Fig. 3: Radial proﬁles of safety factor, temperature, and density of the above DIII-D cyclone test case. The dashed lines indicate the radial simulation box 0.3 ≤ r∕a ≤ 0.7.

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Fig. 4: Benchmarking of TEK code with GENE for the ITG-KBM transition. Upper panel: growth rate; lower panel: angular frequency.

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Fig. 5: ITG-TEM transition benchmarking

Mode structures:

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pict 1.6022d-16 pict

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Fig. 6: ITG n = 20.

ITG-KBM transition:

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Fig. 7: itg-kbm transition, seems to succeed, to be continued. left: real m_e, right: half m_e,(3) increase radial resolution bottom left: δϕ, bottom right: δA_∥.

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