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SUMMARY:Relativistic Electrons’ Orbit Trajectory Calculation and Calcula
tion Study analysis in Electron Cyclotron Heating and Current Drive of Tok
amak Plasmas
DTSTART;VALUE=DATE-TIME:20210511T162500Z
DTEND;VALUE=DATE-TIME:20210511T164500Z
DTSTAMP;VALUE=DATE-TIME:20211028T111412Z
UID:indico-contribution-17242@conferences.iaea.org
DESCRIPTION:Speakers: Md Mahbub Alam (ICS\, Bangladesh Atomic Energy Commi
ssion\, Dhaka\, Bangladesh)\nThe electron cyclotron heating (ECH) is one o
f the intense methods of non-inductive plasma current drive (CD). The ECH
waves accelerated the electrons with the Doppler-shifted electron cyclotro
n resonance (ECR) interactions\, and effectively ramped and sustained the
plasma current non-inductively to achieve long discharge duration. The pla
sma sustainment with ECH waves is a key issue for the steady state operati
on in the tokamak configuration. The plasma was sustained for more than 2
hours by the ECH/CD non-inductive method in the Q-shu University experimen
t with steady-state spherical tokamak (QUEST) [1]. The plasma current gene
ration as well as sustainment of the plasma is strongly related to the ECR
conditions and confinements of the electrons in the magnetic field. In th
is study\, the relativistic electrons’ orbit trajectories were calculate
d and analyzed under equilibrium magnetic configuration of spherical tokam
ak in the ECH/CD to evaluate the ECR conditions and confinements of the el
ectrons in the magnetic field. A framework with several sets of calculatio
n codes accordingly for various theoretical models was developed with the
EFIT (Equilibrium Fitting) plasma equilibrium to calculate and analyses or
bit trajectories.\n\nThis study observed that a large number of passing re
sonant electrons with initial positive $v_\\parallel$ starting from the hi
gh field side were maintained their orbits outside the last closed flux su
rface (LCFS)\, while all the passing resonant electrons with initial negat
ive $v_\\parallel$ starting from the high field side were maintained their
orbits inside the LCFS. The trapped resonant electrons only being the 2nd
harmonic ECR were maintained banana orbits at the low field side of the t
orus where most of the portions of the banana orbits of initial positive $
v_\\parallel$ were placed outside the LCFS.\n\nIn this study\, the equilib
rium magnetic configuration was obtained from the plasma equilibrium solut
ion using 129x129 (129 grid points in the R direction and 129 grid points
in the $Z$ direction) spatial resolutions EFIT code. The poloidal flux $\\
psi$ and toroidal current density of plasma $J_T$ were calculated by the E
FIT code on the rectangular grid with the external magnetics for constrain
t of a discharge that satisfy the model provided by the Grad-Shafranov equ
ation [2].\n\nThe orbit trajectories of the resonant electrons were calcul
ated and analyzed for the 8.2 GHz electron cyclotron heating and current d
rive waves on the equilibrium magnetic configuration of the Q-shu Universi
ty experiment with steady-state spherical tokamak (QUEST) in the relativis
tic Doppler-shifted ECR. The down-shifted and up-shifted fundamental and s
econd (2nd) harmonic relativistic resonances were considered separately. V
arious parallel and perpendicular velocities to the magnetic field\, $v_\\
parallel$ and $v_\\perp$ were considered from the Doppler-shifted ECR cond
ition for the electrons to be resonant with the ECH waves. The parallel re
fractive index $N_\\parallel$ from -1 to +1 with step 0.1 was taken into a
ccount in the multiple-wall reflection model. The maximum energy of the re
sonant electrons was restricted at 100 keV and calculated the orbits of th
ose electrons whose initial energies were between 1 to 100 keV. The orbit
trajectories of the ECR electron were obtained as contour plot of the reso
nant electron’s energy under the equilibrium magnetic configuration on t
he poloidal cross-section. The energy was expressed in terms of magnetic m
oment and toroidal angular momentum. The energy\, magnetic moment\, and to
roidal angular momentum were conserved in the orbit trajectories. All the
resonant and confined electrons’ orbits trajectories were obtained for v
arious positions of the coordinates $(R\, Z)$\, resonant pitch angles and
parallel refractive index. The number of the step parameters was more than
5\,200000. \n\nThe red and blue contours in figure 1 show the calculated
orbit trajectories on the poloidal cross-section between the $R$ positions
from 0.35 m to 0.53 m and $Z$=0.00 m of the fundamental resonant electron
s. The black and green contours show the closed and opened magnetic surfac
es\, respectively. The numbers of actually calculated orbit trajectories w
ere much more than the orbits shown in the figure. The left and right figu
res show the orbit trajectories of the electrons with initial + $v_\\paral
lel$ and - $v_\\parallel$\, respectively. Figure 2 shows the banana orbits
of the trapped electrons on the poloidal cross-section of the 2nd harmoni
c resonant electrons. The number of actually calculated orbits was much la
rger than the orbits shown in the figure. The left figure shows the banana
orbits of the trapped electrons with initial + $v_\\parallel$. The right
figure shows the banana orbits of the trapped electrons with initial - $v_
\\parallel$. \n\n![Orbit Trajectories of the passing resonant electrons][1
]\n\n\n![Orbit Trajectories of the trapped resonant electrons][2]\n\n\n [
1]: http://www.baecbd.org/diagram/Orbit_Trajectories-1.jpg\n [2]: http://
www.baecbd.org/diagram/Orbit_Trajectories-2.jpg\n\nDepending on the ECR fo
r various conditions\, the resonant electrons were travelled both in the p
arallel and the antiparallel directions to the magnetic field of the tokam
ak. The resonant electrons with initial positive $v_\\parallel$ were trave
lled in the parallel direction to the magnetic field\, while the resonant
electrons with initial negative $v_\\parallel$ were travelled in the antip
arallel direction to the magnetic field. These two types of resonant elect
rons with initial positive and negative $v_\\parallel$ contribute current
in opposite directions\, respectively. A significant number of confined el
ectrons with initial positive $v_\\parallel$ were maintained portions of t
he orbits in the open magnetic surfaces that may cause to shift the plasma
outward along the equatorial plane. In the summary\, several codes requir
ed to calculate and evaluate the ECR as well as orbits have been developed
with the EFIT code. Various criteria of the relativistic ECR conditions w
ere properly taken into consideration for the orbit analysis. Additionally
\, the developed code could be applicable to analyze the $\\alpha$-particl
e (alpha) orbits of the burning plasmas. \n\n1. Hanada K.\, et al 2017 Nuc
l. Fusion 57 126061\n2. Havlicek\, J.\, et al 2007 WDS’07 Proceedings o
f Contributed Papers Part II— Physics of Plasmas and Ionized Media WDS
’07 234-239\n\nhttps://conferences.iaea.org/event/214/contributions/1724
2/
LOCATION:Virtual Event
URL:https://conferences.iaea.org/event/214/contributions/17242/
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