# Tokamak plasma heating current

#### artis

I will make some assertions and then phrase a question , please correct me if necessary.

So the tokamak works like a transformer where the primary is a coil winding while the secondary is a torus which contains plasma which being electrically conductive forms the secondary winding?
The toroidal field coils are there surrounding this "secondary plasma winding" for added plasma stability and to keep it away from vessel walls trying to maintain the charged particle trajectories along the closed B field lines looping around the torus?

Now since I don't see any electrodes physically going inside the plasma torus I assume the plasma ohmic heating is done simply by inducing a current in the "short circuit" one loop secondary which is the plasma.
What frequency is used for this main transformer action ?

I was trying to find but at first hand had no luck , what would be/are the currents in ITER for example in the transformer primary when at full load , maybe someone knows the primary turns and applied voltage/frequency of this transformer?

Anyway the applied current is probably large in order to induce and even larger current in the secondary which is the plasma itself, I was then wondering could reactive power be used here to save some of the energy necessary for plasma heating? Because plasma much like a wire gets heated when more and more current is passing through it and as we know in transmission lines such current can arise from reactive power being transferred back and forth between source and load, I wonder is it possible to create the same scenario in a tokamak transformer where by shifting the current and voltage out of phase in the secondary one could maintain high current but lower the total energy consumed in the secondary which seems like a short circuit otherwise. The plasma to the best of my knowledge behaves like a low resistance resistor and the heat dissipated in a resistor is proportional to current so would shifting the voltage and current out of phase help in reducing total energy consumed or would it simply decrease the current through the plasma and defeat any such attempt at conserving some of the applied power, because of ohms law where lover voltage through a resistor causes lower current?

just a curiosity

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#### trurle

The overview on ITER plasma heating system can be found in
https://www.burningplasma.org/ref/aps_rasmussen_ITER_nov11.pdf

Overall, as expected for experimental reactor, the heating system is complex and likely redundant.
Expected operation mode is to heat first by particle injection, and then further heat plasma by RF wave resonating with free electrons in plasma. Frequency of RF excitation must be variable as plasma resonant frequency changes during heating and compression.

#### phyzguy

Now since I don't see any electrodes physically going inside the plasma torus I assume the plasma ohmic heating is done simply by inducing a current in the "short circuit" one loop secondary which is the plasma.
What frequency is used for this main transformer action ?
I think you are visualizing the primary winding being driven by an AC current, which induces an AC current in the plasma. This is not correct. This doesn't work, because when the AC current goes to zero, the plasma current goes to zero and the confinement fails. So what is done is that the primary winding is driven by a ramped DC current, which increases linearly with time. This induces a constant current in the plasma as long as you continue to ramp the current in primary. Eventually you reach a limit where you can't ramp the primary current any higher, at which point you stop and start over with a new plasma. ITER is designed so that the primary current ramps steadily for 400 seconds, which is called a "burn time". Then you stop, flush out the plasma chamber, inject new fuel, and start a new ramp. The design specs give the induced current in the plasma during the 400 second ramp as 15 MegaAmps. Does this clear it up?

#### artis

Interesting, so you say the current ramps up linearly but how can it ? 400 seconds is quite long it would make for a very low frequency large pulse so I think that probably the current is ramped up with some clever waveform although I can't imagine now how could it look like.

I wonder why can't they use maybe some higher frequency (Khz) AC and maybe from two sources (two windings) and adjust so that there is essentially no deadtime , that wouldn't destroy the plasma confinement or would it ?

So do they use neutral particle injection and RF heating much more at the beginning of each burn time because the heating current from the transformer is "small" at beginning?

#### phyzguy

Why can't it ramp linearly? I don't know why you call it "a very low frequency large pulse", it is not a pulse, it is a linear ramp. If the primary current ramps linearly, then the B field in the transformer ramps linearly, so $\partial B / \partial t$ is constant and the current induced in the plasma is constant. They do use auxiliary sources of heating such as neutral beams, but these are used throughout the cycle, since the plasma current is basically constant.

Look it up somewhere. For example, here is a quote from Wikipedia,

"The current is induced by continually increasing the current through an electromagnetic winding linked with the plasma torus: the plasma can be viewed as the secondary winding of a transformer. This is inherently a pulsed process because there is a limit to the current through the primary (there are also other limitations on long pulses). Tokamaks must therefore either operate for short periods or rely on other means of heating and current drive."

#### trainman2001

Is ITER actually functioning? The last I heard that it was behind schedule and way over budget. I had the opportunity to visit the Princeton Tokamak with my son in late 80s. It was the closest thing I could imagine that looked and felt like a sci-fi Hollywood set.

#### phyzguy

Is ITER actually functioning? The last I heard that it was behind schedule and way over budget.
Not yet. I think it is in fact "behind schedule and way over budget".

#### artis

But wiki that you quoted also says "long pulse". It is just that when you give the confinement time of about 400 secs and a current that continually rises through those 400 secs, then I wonder how slow is the rise time , if it was part of a sine wave how low would be the frequency?

#### phyzguy

I don't know those details. You'd have to dig into the design of ITER, or perhaps a functioning tokamak like JET.

#### artis

I also wonder how efficient this tokamak transformer is with respect to energy in primary vs energy induced in secondary (the plasma) because unlike a conventional wire winding which is as close as possible to the core , the plasma I assume is further away and has various metals inbetween the core and the plasma which would be the plasma vessel, toroidal field coils etc.
I wonder can someone comment here more on this topic.

"Tokamak plasma heating current"

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