Beam in Plasma

Beam stopping and shine-through power in BTR-code

The new BTR version (BTR 3.0) implements a simple model of thin beam ionization in tokamak plasma and calculates the shine-through power footprint on the FW. The injected beam decay is assumed exponential along the beam axis.

Thin beam approximation: NB cross-section is much less than plasma minor radius a. NB attenuation along X:

I₀ – injected current;

σ – total ionization cross-section;

n – plasma density;

X₀ – NB entry point to plasma.

The branches of NB ionization:

H⁺ + H -> H⁺ + H⁺ + e - ionization on plasma ions

e + H -> H⁺ + 2e - ionization on plasma electrons

H⁺ + H -> H + H⁺ - charge exchange collision with ions

NB ionization = direct + cascade (multi-step) ionization

Beam stopping cross-section enhancement:

δ ~20% (E ≤ 80keV/n), ~100% (E ≥ 600keV/n)

The tangential injection point is defined by the tokamak position (X, Y, Z) in NBI frame. The following parameters are added to BTR Input List (Green panel, section “Tokamak area”):

Tokamak Centre X in NBI frame, m

Tokamak Centre Y in NBI frame, m

Tokamak Centre Z in NBI frame, m

Tokamak Sectors Number

Plasma density (n) and temperature (Te) profiles along radius are assumed parabolic (BTR 3.0), with the possibility to set their heights. The ionization cross-sections (CS) are calculated automatically based on the preloaded tables. The tables of Cross-sections and rate coefficients (per nucleon) are taken from Culham Lab data (Atomic Collision Processes in Plasma Physics experiments, 1974. R.L.Freeman, E.M. Jones)). Impurities are not included, multi-step factor can be varied (0…1).

For the shine-through particles position of the point where the neutral hits the FW is calculated according to latest 2D FW geometry (S. Putvinski, SIMPLIFIED 2D AND 3D FIRST WALL MODELS FOR ANALYSIS OF ENERGETIC PARTICLE LOSS, IDM).

2D wall contour. Table1 shows 2D contour data of ITER first wall. The wall contour consists of straight segment – one for each blanket module. In this approximation the wall is axi-symmetrical and each segment is conical surface.

Tab. 1 Coordinates of 2D wall contour (FW)

Simplified 3D wall geometry. Actual ITER wall has wall tiles which are shaped to minimize heat loads during flat top operation. Two options - “5 facet” wall shape and simplified “3 facet” are suggested. The 3D wall structure proposed is periodic toroidally with period 20 degree.

BTR uses a simplified (“1-facet”) 3D wall structure, which is periodic along toroidal axis. The number of toroidal sectors (i.e. the angular step) is the input value (Tokamak Sectors Number). The resulting tetragonal mesh is covered with flat cells (“tiles”) – as shown in Fig.2.

Fig.2 BTR plot with tokamak FW model. 3 toroidal sectors (10^o each) are shown with “tiles”. Red - selected (calculated) tiles.