Transport simulation of ITER (International Thermonuclear Engineering Reactor) startup Page: 2 of 3
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'•'tot ”'•'int + '•'ext* '*'mhd + ’•’res " '•'s ,
where Vm is the total magnetic flux nipplied by the bansfcnner
core, '•'ini it the poloidal flux in the plasma, '•'ext u the external flux,
'•Vital >* the flux dissipated as a consequence of sawteclh, '•'res is the
resistive flux loss, and V| is the current source tenn. About 203
V-s is requited to reach the operating point, of which about 31 V-s is
dissipated by plasma resistivity and sawteeth. The flux savings due
to turning on the beam prior to the end of the current ramp were on
the order of 3.1 V-s. This is due primarily to reduced resistance
from !.c»ting and not to beam-driven current.
Figures 2(a) and 2(b) show the evolu tion of the profiles of
electron tempentuic And density, respectively. Siwiooth activity
begins to be visible at about 23 s, when the current is around 11 MA.
The electron density is centrally peaked because of deuterium from
the beams after they are twned.QQ.at SO i.. _
The total toroidal current density profile is limited in the core by
the sawtooth model, as shown in ng.2(cV The current tirup is
slow enough to avoid skin currents. Note that the source current
iknsity from benm injection [Fig. 2(d)] is more peaked dun the total
current density and actually is much larger than the total current
density on axis. Such a case results in a negative emf in the plasma
E«q( Jtotal- Jsource) •
The total current density tries to respond on a resistive time scale by
becoming more peaked, but sawteeth prevent the central cutrem
density from increasing far very long. The whole picture is
complicated by bootstrap currents, which contribute to the source
term in a way that depends on the local density ind temperature
The volt-second consumption by sawteeth could be reduced if the
source current density could be flalieried sufficiendy, perhaps by
aiming the beams a little farther away fiom the axis. In the present
esses, the beam is injected at a 4.6° ingle to the horizontal midpline.
snd it crosses the midpUne Q.8 m inboard of the major radius. Pci
these simulations, no effort was made to eliminate sawteeth by
varying the injection geometry, although we have demonstrated
elsewhere that this is possible to soote degree.5 In general, the
optimum injection geometry depends on the plasma density; one must
consider whether the shinethrough during startup is too large, as well
as whether the current source prefile is too peaked. The addition of
lower hybrid tr other current-broadening sources would permit in
optimal current source prefile to he achieved more easily.
At steady stare, beta is near the critical value (4.7%). and Q s 5.
The bootstrap effect provides shout 10% of the total current, and the
current drive efficiency is around 0.2 A/W.
For the ITER Physics Phare (R » 5.8 m, a « 2.2 m, ic = 1.88,
B = 5.0 T, I = 22 M.t), the current is ramped at the same rate as for
the Technology Phase but is continued out to 80 s to achieve the
operating current of 22 MA. After full current is achieved, 50 MW
of 1-MeV beams is turned on for 20 s. Figure 3(a) shows the
average and peak electron and ion temperatures during the startup and
the initial part of the bum. The avenge electron density [Fig. 3(b)) is
tamped to encourage cutrem penetration without causing a thermal
collapse, as described in the preceding section. At 100 s, the ignited
operating point is reached and no funner beam hating is required.
The poloidal flux required during the startup ind initial bum is
shown in Fig. 3(c). About 270 V-s is required to reach the operating
point, of which about 58.7 V-s was dissipated by plasma resistivity
and sawteeth. The sawtooth contribution is larger than that for the
Technology Phase because of the higher current, which tends to
decrease q an axis. During the bum. flux is dissipated at about 0.06
(V-sVs, which must be supplied inductively. This should be
regarded as m estimate; evaluating accurately the rate of flux
dissipation over many hundreds of sawtooth periods while
incorporating the slow relaxation of the current profile is a
numerically difficult problem that is sensitive to the physical details
of the sawtooth model.
Figures 4(a) and 4(b) show the evolution of the profiles of
snout 14 MA. Since the beam power is lower than that for die
Technology Phase, the fueling by the beam U less. This lower beam
fueling, together with the braider sawtooth region due to the higher
operating current, prevents peaking of die density profile.
The total toroidal cturent density profile (Fig. 4(c)) shows no
significant effect from the source due to beam heating (Fig. 4(d)].
The source is much smaller than that far the Technology Phase
because of tie reduced beam power and the higher target plasma
At the operating point, bets is near the critical vilue (6%), and the
bootstrap effect provides about 14% of the total current.
Fig. 2. Technology Phase fxtrfiles of (a) electron temperature, |b) electron density, (c) total current density, and (d) beam-driven current
density vs time.
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Attenberger, S.E. & Houlberg, W.A. Transport simulation of ITER (International Thermonuclear Engineering Reactor) startup, article, January 1, 1989; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc1093721/m1/2/: accessed March 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.