Abstract
The dynamics of the neutral beam injection fast ions in the TJII stellarator is studied in this paper from both the theoretical and experimental points of view. The code Integrator of Stochastic Differential Equations for Plasmas (ISDEP) is used to estimate the fast ion distribution function in 3D:1D in real space and 2D in velocity space, considering the 3D structure of TJII, the electrostatic potential, non turbulent collisional transport, and charge exchange losses. The results of ISDEP are compared with the experimental data from the compact neutral particle analyzer, which measures the outgoing neutral flux spectra in the energy range .
The authors would like to thank the Spanish Science Ministry for the financial support under Project Nos. ENE200806082/FTN and ENE201019676 and José Guasp and Luis Esteban for fruitful discussions.
I. INTRODUCTION
II. THE CNPA DETECTOR IN TJII
III. THE ISDEP CODE
IV. RECONSTRUCTION OF THE CNPA FLUX SPECTRUM
V. ESTIMATION OF THE ABSOLUTE CNPA SIGNAL
VI. CONCLUSIONS
Key Topics
 Particle distribution functions
 10.0
 Radiation detectors
 6.0
 Magnetic field sensors
 5.0
 Plasma density
 5.0
 Charge exchange reactions
 4.0
H05H1/02
Figures
Geometrical scheme of the NBI lines and line of sight of the CNPA in TJII (top view). In TJII, the plasma column has a vertical excursion of every period ( ), so the CNPA LOS does not look straight to NBI .
Geometrical scheme of the NBI lines and line of sight of the CNPA in TJII (top view). In TJII, the plasma column has a vertical excursion of every period ( ), so the CNPA LOS does not look straight to NBI .
CNPA channels and energy width (error bars in the plot, usually smaller than the symbols) and efficiency. Measurements in the low energy channels are not precise because these channels overlap in energy.
CNPA channels and energy width (error bars in the plot, usually smaller than the symbols) and efficiency. Measurements in the low energy channels are not precise because these channels overlap in energy.
Plasma parameters (effective radius, inclination of the field lines, and neutral density) as a function of the distance x along the LOS (sector B2, tangential port).
Plasma parameters (effective radius, inclination of the field lines, and neutral density) as a function of the distance x along the LOS (sector B2, tangential port).
Left plot: plasma profiles used in ISDEP for the comparison with the CNPA: density, electron and ion temperatures, electric potential, and neutral density. Right plot: Spitzer slowing down time, ^{ 4 } showing that the typical timescale of this system is a few milliseconds.
Left plot: plasma profiles used in ISDEP for the comparison with the CNPA: density, electron and ion temperatures, electric potential, and neutral density. Right plot: Spitzer slowing down time, ^{ 4 } showing that the typical timescale of this system is a few milliseconds.
Left plot: cross sections for the atomic processes in the fast ion detection. ^{ 15 } The charge exchange ( ), ionization protons impact ( ) and electron impact ( ) cross sections are expressed in terms of the fast particle energy (E). The ionization by electron impact rate ( ) depends on the background electron temperature T_{e} . In this case, it is plotted for . Right plot: dependency of the electron impact ionization rate coefficient with the electron temperature. It is approximately constant for the TJII electron temperatures in NBI discharges ( ).
Left plot: cross sections for the atomic processes in the fast ion detection. ^{ 15 } The charge exchange ( ), ionization protons impact ( ) and electron impact ( ) cross sections are expressed in terms of the fast particle energy (E). The ionization by electron impact rate ( ) depends on the background electron temperature T_{e} . In this case, it is plotted for . Right plot: dependency of the electron impact ionization rate coefficient with the electron temperature. It is approximately constant for the TJII electron temperatures in NBI discharges ( ).
Charge exchange time in TJII, according to Eq. (4) , in the conditions considered. It turns out that CX processes are not negligible only in the external part of the plasma and for low energies, where is short enough. Since ISDEP deals with orbits in the SOL, where is calculated in the SOL assuming that the profiles of plasma parameters are constant in the SOL and equal to their value at .
Charge exchange time in TJII, according to Eq. (4) , in the conditions considered. It turns out that CX processes are not negligible only in the external part of the plasma and for low energies, where is short enough. Since ISDEP deals with orbits in the SOL, where is calculated in the SOL assuming that the profiles of plasma parameters are constant in the SOL and equal to their value at .
Left plot: line density, Xrays and NBI traces for shot #18982. Right plot: CNPA raw data for selected channels (see Fig. 2 for the energy associated to each channel and its width). For this shot, a 30 ms plateau is found in the signals. We can find a low error flux spectrum averaging each channel in time and taking the mean with similar shots.
Left plot: line density, Xrays and NBI traces for shot #18982. Right plot: CNPA raw data for selected channels (see Fig. 2 for the energy associated to each channel and its width). For this shot, a 30 ms plateau is found in the signals. We can find a low error flux spectrum averaging each channel in time and taking the mean with similar shots.
Steady state distribution function for TJII with the profiles shown in Fig. 4 for (top, left); (top, right); (bottom, left), and (bottom, right). Traces of the injected ions at 10, 15, and 30 keV can be seen. The distribution function is normalized so . The statistical error in f depends on the value of f, see Fig. 9 .
Steady state distribution function for TJII with the profiles shown in Fig. 4 for (top, left); (top, right); (bottom, left), and (bottom, right). Traces of the injected ions at 10, 15, and 30 keV can be seen. The distribution function is normalized so . The statistical error in f depends on the value of f, see Fig. 9 .
Relative statistical errors in f (see Fig. 8 ), in %.
Comparison of the flux spectrum measured by the CNPA and calculated with ISDEP. Both flux spectra are normalized to one for . In the CNPA spectrum, the error bars are the standard deviation of the measurements of the different discharges. In the ISDEP curve, the error bars are the Monte Carlo statistical errors. The error bars are smaller than the symbol size for many points in the spectrum. The persistence of fast ions P(t) is shown in the small chart indicating the existence of two timescales: small NBI direct losses around and CX or hits to the vacuum vessel at larger times.
Comparison of the flux spectrum measured by the CNPA and calculated with ISDEP. Both flux spectra are normalized to one for . In the CNPA spectrum, the error bars are the standard deviation of the measurements of the different discharges. In the ISDEP curve, the error bars are the Monte Carlo statistical errors. The error bars are smaller than the symbol size for many points in the spectrum. The persistence of fast ions P(t) is shown in the small chart indicating the existence of two timescales: small NBI direct losses around and CX or hits to the vacuum vessel at larger times.
Plasma profiles for a low density NBI shot (left). CNPA spectra and ISDEP simulation (right).
Plasma profiles for a low density NBI shot (left). CNPA spectra and ISDEP simulation (right).
Tables
Plasma volume, average minor radius, and iota range (from the axis to the edge) for the two magnetic configurations considered.
Plasma volume, average minor radius, and iota range (from the axis to the edge) for the two magnetic configurations considered.
Comparison of absolute values of the fast neutral spectra at 10 keV. Errors are indicated in parentheses.
Comparison of absolute values of the fast neutral spectra at 10 keV. Errors are indicated in parentheses.
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