Last week, PSS Mike Paluszek visited ITER, the international fusion research experiment under construction in France. In light of Mike’s recent visit to ITER, we wanted to showcase an application of our tokamak Fusion Reactor Design function to the design of ITER. This function is part of the Fusion Energy Toolbox for MATLAB, a toolbox that includes a variety of physics and engineering tools for designing fusion reactors and studying plasma physics. We will also compute design parameters for ITER’s successor, the DEMOnstration power plant (DEMO), a fusion reactor currently in the design phase which is planned to achieve net electricity output.

We first apply the Fusion Reactor Design function to ITER. Note that ITER is expected to produce 500 Megawatts (500 MW) of *fusion power*, but this will not be converted into *electric power*, the power that goes into the electrical grid. DEMO, on the other hand, is planned to produce 500 MW of *electric power* from 2000 MW of *fusion power*. The Fusion Reactor Design function asks for the net electric power output of the reactor, P_E, as an input, so we generate a value for P_E for ITER by using the same ratio of electric-to-fusion power as in DEMO, giving us a P_E of 125 MW for ITER. The inputs used for the ITER design are shown below (see references [1,2]), where we use a data structure “d_ITER”:

```
d_ITER.a = 2; % plasma minor radius (m)
d_ITER.B_max = 13; % maximum magnetic field at the coils (T)
d_ITER.P_E = 125; % electric power output of the reactor (MW)
d_ITER.P_W = 0.57; % neutron wall loading (MW/m^2)
d_ITER.H = 1; % H-mode enhancement factor
d_ITER.consts.eta_T = 0.25; % thermal conversion efficiency
d_ITER.consts.T_bar = 8; % average ion temperature (keV)
d_ITER.consts.k = 1.7; % plasma elongation
d_ITER.consts.f_RP = 0.25; % recirculating power fraction
```

The first five inputs were described in our original post on the Fusion Reactor Design function. The function can be called to perform a parameter sweep over any of these inputs. We also specify values for some constants: the thermal conversion efficiency ‘eta_T’, the average ion temperature ‘T_bar’, the plasma elongation ‘k’, which is a measure of how elliptical the plasma cross-section is, and the recirculating power fraction ‘f_RP’. We can perform a parameter sweep over the minor radius (from a = 1.8 meters to a = 2.2 meters, with 100 points in between) and display a table of results simply with two lines of code:

```
d_ITER = FusionReactorDesign(d_ITER,'a',1.8,2.2,100); % run function
d_ITER.parameters % show table of resulting parameters
```

Looking at the results table from d_ITER.parameters, we see overall agreement with parameters for ITER [1,2]. The plasma major radius (essentially the tokamak radius) R_0 output is about 5 m, which is in the ballpark of the 6.2 m radius of ITER design, and the magnetic field at R_0 (on plasma axis) output is 4.8 Tesla, close to the ITER design value of 5.3 Tesla. The plasma current output is 17.5 MegaAmps, which is also close to ITER’s design of 15 MegaAmps.

The Fusion Reactor Design function also outputs plots that show whether or not the reactor satisfies key operational constraints for tokamaks, see the figure below. The first three curves check various constraints to ensure the plasma is stable, which we see are met as they are located in the unshaded region (though the green curve is marginally close to the constraint boundary). The blue curve’s position deep into the shaded region indicates that the reactor is far from producing enough electric current to sustain itself. The designers of ITER anticipated this, which is why ITER will additionally use a pulsed inductive current and test a combination of other techniques to drive the plasma current.

We now consider DEMO, which is in the design phase with the goal of net electrical power output. Similarly to running the ITER case, we set up a data structure (now called ‘d_DEMO’) with known DEMO input parameters [3] and perform a parameter sweep over the minor radius ranging from a = 2.7 meters to a = 3.1 meters:

```
d_DEMO.a = 2.9; % plasma minor radius (m)
d_DEMO.B_max = 13; % maximum magnetic field at the coils (T)
d_DEMO.P_E = 500; % electric power output of the reactor (MW)
d_DEMO.P_W = 1.04; % neutron wall loading (MW/m^2)
d_DEMO.H = 0.98; % H-mode enhancement factor
d_DEMO.consts.eta_T = 0.25; % thermal conversion efficiency
d_DEMO.consts.T_bar = 12.5; % average ion temperature (keV)
d_DEMO.consts.k = 1.65; % plasma elongation
d_DEMO.consts.f_RP = 0.25; % recirculating power fraction
d_DEMO = FusionReactorDesign(d_DEMO,'a',2.7,3.1,100); % run function
d_DEMO.parameters % show table of resulting parameters
```

The outputs for the DEMO case also show overall agreement with DEMO parameters [3]. The plasma major radius R_0 output is 7.8 m, which is not far from the 9 m design radius for DEMO. The resulting on-axis magnetic field output is 6.2 T, close to the 5.9 T of the DEMO design. The plasma current output is now 21 MegaAmps, which is less than 20% away from the design value of 18 MegaAmps. It is important to note that in each of these parameters, we see an increase going from ITER to DEMO, which is consistent both in our model’s output and the actual design parameters in the papers [1-3].

The operational constraints plot for DEMO is shown in the figure below. DEMO is a larger reactor than ITER, and given the favorable scaling of tokamak operation with size, we expect improved results for operational constraints in DEMO. The three curves which check plasma stability are all satisfied. Unlike in the case of ITER which had the green curve close to the shaded region, the green curve in the case of DEMO stays safely in the unshaded region. The blue curve is still in the unshaded region, but much closer to the boundary of the unshaded region than ITER (now ~1.8, much closer to 1 than in the case of ITER which was ~4). This shows an improvement for DEMO compared to ITER as it is closer to producing enough self-sustaining plasma current, though it will still need some help from other current-generating techniques which will be tested on ITER.

This function is part of release 2022.1 of the Fusion Energy Toolbox. Contact us at info@psatellite.com or call us at +01 609 275-9606 for more information.

[1] Aymar, Barabaschi, and Y Shimomura (for the ITER Team), “The ITER Design”, Plasma Physics and Controlled Fusion 44, 519–565 (2002); https://doi.org/10.1088/0741-3335/44/5/304

[2] Sips et al., “Advanced scenarios for ITER operation”, Plasma Physics and Controlled Fusion 47 A19 (2005); https://doi.org/10.1088/0741-3335/47/5A/003

[3] Kembleton et al., ” EU-DEMO design space exploration and design drivers”, Fusion Engineering and Design 178, 113080 (2022); https://doi.org/10.1016/j.fusengdes.2022.113080

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