There are three main conditions to obtain ignited plasma:

  • 1. The plasma ions must be hot enough to overcome Coulomb force during the collisions between D and T ions. For D-T plasma in magnetic fusion, the temperature of plasma ions should be in the range of T:~ 10-30 keV;
  • 2. Hot plasma must be insulated from the walls, and the plasma energy confinement time defined as rE=Plasma energy/Heat loss should be long enough. Here, plasma with its energy content W=nTV (V is the volume of plasma) cools down as

in the absence of any heating sources;

3. The fuel densities nD and nT must be high enough that fusion reactions occur at a suitable rate. Maximum plasma density is limited by impurities and instabilities.

For the particular case of D-T fusion in a magnetic camera, the criterion of plasma ignition for self-sustaining fusion reaction (similar to the Lawson criterion in inertial fusion) is expressed as a triple-product criterion [1.3]:

The dimension of the triple-product (pressure x time) shows that thermonuclear-grade plasma must be confined at a pressure of approximately 10 atm for 1 s. This range lies between the fusion conditions achieved in the Sun and stars, and those achieved in inertial fusion. Note here that the criterion (1.6) is only a necessary condition for ignition. It was obtained under the most optimistic assumptions.

For performing a wide range of physics experiments w'ith fusion-grade plasmas, for example, for developing plasma heating systems and plasma scenarios, pure deuterium plasmas are often used. These generate D-D neutrons and can be used for assessing the fusion performance of DT plasma. Such D-only experiments do not require enhanced protection from 14 MeV neutrons and tritium.

Since the 1970s, significant progress has been achieved in maximising the triple-product (1.6) in equivalent D-only plasmas. This progress can be summarised as follows:

  • 1970 - 25,000 times too small for ignition;
  • 1983 - 100 times too small;
  • 1995 - only five times too small.

Figure 1.4 shows how the progress in the triple-product was achieved historically, and what ion temperatures were achieved together with the triple-product values.

Two magnetic fusion machines, TFTR (United States) and JET (European Union), also conducted experiments with real D-T plasmas. The following fusion power levels in D-T plasma have been achieved:

  • 1991 - JET - 1.7 MW (10% T; 10 MW heating)
  • 1995 - TFTR - 10 MW (50% T; 40 MW heating)
  • 1997 - JET - 16 MW (50% T; 22 MW heating)"

We now express the ignition criterion (1.6) in engineering terms, which include magnetic field В and normalised plasma pressure B=Pr,„.„JP„„c.„..„=4un(nT)/B2 of a fusion machine. By multiplying and dividing (1.6) by B2, we obtain

Expression (1.7) shows that the ignition may be achieved along three avenues:

Increasing energy confinement time r£;

Increasing magnetic field B

Increasing /7.

We now consider each of these options.

Magnetic fusion progress in maximising triple-product in equivalent D plasma

FIGURE 1.4 Magnetic fusion progress in maximising triple-product in equivalent D plasma.

Increasing Energy Confinement Time tE

Development along this avenue corresponds to a larger volume V of the fusion reactor. Indeed, when the plasma energy balance is determined by the alpha particles heating alone (in the ignited state), with the alpha particle power of Pa=0.2 FVusiopa for a steady-state operation of the fusion reactor, d/dr= 0, one obtains

so that

From (1.9) we see that for a given pow'er of PFUSion> achieving ignition by increasing rE means a machine with a larger volume V as the plasma temperature and density are optimised for fusion conditions and neither could be varied significantly for increasing rE. In particular, for a magnetic fusion reactor generating P|:USK)N= 1 GW (typical value of a large industrial city), the volume of the D-T plasma should be approximately V~ 1000 m3. It follows from this estimate that:

A. The next step international project ITER [1.5,1.6] will approach the critical volume required for the ignition very closely;

B. Among all magnetic fusion machines in operation, Joint European Torus (JET) [1.7] has the largest volume of V~ 100 m3, which is an order of magnitude below the ignition-size volume, as shown in Figure 1.5. This means that present-day magnetic fusion experiments are being developed with subcritical volumes. Such fusion research is similar to fission research if the critical mass could not be achieved.

Increasing Magnetic Field В

It is technologically challenging to obtain B>5 T. The engineering constraints on the coil’s structural integrity generating the magnetic pressure В212ц0 become very severe as the magnetic pressure is= 1 kg/cm2 for В = 0.5 T, but it becomes «400 kg/cm2 for В = 10 T. Several projects were developed aiming at increasing B, including the present-day tokamak Alcator C-MOD (United States). Several next-generation machines were also designed, for example, IGNITOR (Italy) and FIRE (United States). Recent development of high-temperature super-conducting magnets may significantly enhance this avenue of magnetic fusion development in the future.

Increasing Beta

The beta parameter shows how much plasma pressure per unit magnetic pressure could be confined in a magnetic fusion machine. The maximum value of this parameter is limited by magneto- hydrodynamic (MHD) instabilities, typically at a level of few percent, in present-day machines. In contrast to the technological difficulties in the first two avenues of approaching the triple-product ignition criterion, high volume and high B, the beta limit is determined by laws of physics. Instead of the technological improvements, an optimisation of the magnetic field topology could be the key to achieving higher values of beta.

The search for the best topology of magnetic field in tokamaks capable of achieving high beta resulted in the concept of a spherical tokamak (ST) with comparable minor and major radii, R/a~ l,

Comparison of plasma cross-sections for some of the machines on the way to ITER

FIGURE 1.5 Comparison of plasma cross-sections for some of the machines on the way to ITER.

Comparison of small and large aspect ratio toroidal geometries

FIGURE 1.6 Comparison of small and large aspect ratio toroidal geometries.

as shown in Figure 1.6. Such machines achieved volume averaged beta up to {())«40%, which is an order of magnitude higher than the machines with typically large aspect ratio of R/a-Ъ. The advantages of the ST concept in achieving high beta are demonstrated in present-day machines MAST (United Kingdom) and NSTX (United States), and the next step project STEP (United Kingdom) is currently being developed.


The ultimate aim of the magnetic D-T fusion is self-heating of thermonuclear plasma by fusiongenerated alpha particles, so the role of energetic alpha particles in magnetic fusion is key. A good confinement and predictable cross-field transport of these alpha particles are absolutely essential for successful fusion, so it is important to investigate in depth the transport processes involving fusion-generated alpha particles that heat the plasma. Energy of alpha particles born in D-T fusion reactions, 3.52 MeV, exceeds the temperature of thermal ions more than hundred times. Therefore, alpha particle populations that will have much lower density than the thermal plasma, njne< 1%, in DT plasma experiments like ITER, will have its energy content, na E„, about ~10%-15% of the thermal plasma energy content. This implies that alpha particles could notably affect MHD instabilities driven by thermal plasma pressure, and could excite new' types of kinetic instabilities associated with alpha particle motion at speeds much higher than those of the thermal ions. Instabilities of weakly damped toroidal Alfven eigenmodes (TAEs) are of particular concern as alpha particles have birth velocity exceeding Alfven speed. During the slowing down, alpha particles enter resonance with TAEs and may excite TAEs due to the free energy source in alpha particle pressure gradient. If TAE amplitudes driven by alpha particles do not saturate at a negligibly low level, TAEs could significantly affect the cross-field transport of alpha particles; thus, making predictions of alpha particles in fusion plasmas more uncertain and difficult.

Apart from alpha particles, other types of energetic particles are often used in auxiliary heating of plasma to increase thermal plasma temperatures. Plasma heating with energetic ions produced from neutral beam injection (NBI) and/or ion cyclotron resonant heating (ICRH) are effective techniques widely used in present-day machines.

Finally, additional currents generated by energetic particles under certain conditions are often a valuable asset for controlling magnetic field topology in the plasma.

All these issues will be discussed further in this book. We end this introductory section with Table 1.1 demonstrating which parameters of fusion alpha particles and auxiliary heating systems have been achieved in present-day experiments, and how these compare with similar parameters expected on ITER (Table 1.1).


Fast Ion Parameters for Various Tokamak Heating Systems



P, (0) (MW/m)

n, (0)/n,.(0) (%)

fit (0) (%)


Max RVP,















= 1-2

Alpha particles TFTR3







Alpha particles JETC














* Parameters in TFTR DT discharge #76770 with 40 MW of 100 keV NBI, B,=5 T.

b Typical parameters achieved in JET deuterium plasmas with up to 15 MW of ICRH ’He minority heating with ’He tail temperature {£,)= I MeV.

c Alpha particle parameters in JET record high fusion power (16.1 MW) H-mode DT discharge #42976 with 22 MW of NBI and 3.1 MW of ICRH. Br= 3.6 T.

d The anticipated alpha particle parameters of the "Ignited ITER” Project considered before 2000 [1.8].


L.A. Artsimovitch, Controlled thermonuclear reactions, Gordon and Breach, New York (1974). G.H. Miley et al.. Fusion Cross-Sections and Reactivities, Univ. of Illinois Nucl. Eng. Report COO-2218-17. Urbana. IL (1974). J. Wesson, Tokamaks, Oxford University Press, Oxford, 4th Edition (2011). V.D. Shafranov, Physics - Uspekhi 44 (2001) 835. 5. ITER Physics Basis. Nucl. Fusion 39 (1999) 2137. 6. Progress in the ITER Physics Basis, Nucl. Fusion 47 (2007) SI. 7. P.H. Rebut et al., Proceed, of the 10th Intern. Conf, Plasma Physics and Controlled Nuclear Fusion,London (IAEA. Vienna. Vol. I. 1985). p. 11. 8. J. Jacquinot et al., Nucl. Fusion 39 (1999) 2471.

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