CONTROLLED THERMONUCLEAR FUSION Nuclear energy E = m c Fusion Fission 1 Main CTF Reactions DD, DT, DHe 3 Reactions D + D D + T D + He 3 T (1 MeV) + p (3 MeV) - 5 % He 3 (.8 MeV) + n (.45 MeV) - 5 % He 4 (3.5 MeV) + n (14.1 MeV) He 4 (3.7 MeV) + p (14.7 MeV) - D (deuterium) hydrogen stable isotope,.15 % content in water. - T (tritium) hydrogen instable isotope, coming from: Li 6 + n He 4 ( MeV) + T(.7 MeV) Li 7 + n He 4 + T + n -.5 MeV - Li (lithium) natural element with isotopes: Li 6-7.4 % and Li 7-9.6 % in nature. 1
Magnetic Confinement of Fusion Plasmas: The charged particles, the ions and the electrons, are confined by the magnetic fields, the neutrons escape from the plasma volume. I(B z ) I(B tr ) CTF Reactions Secondary reactions present with the primary DT reaction: T + T He 3 + He 3 He 4 + n + 11.3 MeV He 4 + p + 1.9 MeV T + He 3 He 4 + n + p + 1.1 MeV [51 %] He 4 + D + 14.3 MeV [43 %] He 5 + p + 14.3 MeV [6 %] He 4 + n 4
CTF Reactions without neutrons The energy released by the fusion reaction given to neutrons escapes from the plasma as they are not contained by the magnetic field. The following fusion reactions do not have neutrons as products: p+ B 11 3He 4 (8.66 MeV) p+ Li 6 He 3 (.3 MeV) + He 4 (1.7 MeV) In this case the energy released by the fusion reaction is given to charged particles only and remains inside the plasma as they are contained by the magnetic field. 5 CTF Reaction cross sections 6 3
Coulomb barrier When the nuclei of to atoms, that are both positively charged, approach, the repulsive Coulomb force acts. At R this force is replaced by the attractive nuclear force replace the Coulomb force. Then fusion of the two nuclei in a new nucleus. The energy due to the Coulomb force to reach the distance r between the nuclei is Z1Ze W = 4 r Thus in order to reach the distance R to have fusion the energy to be supplied to the nuclei is: W Z1Ze = 4 R ZZe 1 4e R R r 7 f v = CTF Reaction integrals R f nn 1 + = f ( v ) f ( v ) v - v ( v - v ) d v d v 1 1 1 f 1-1 3 m s 8 4
Energy balance in CTF Energy gain due to the fusion reactions: P f = n 1 n < f v> Q P f, = n 1 n < f v> Q where Q and Q are the total energy and the energy of the particles (He 4 ) respectively released by a fusion DT: Q = 3.5 MeV and Q = 17.6 MeV) 9 Energy balance in CTF Radiation losses: When hydrogen isotopes are present, there are not line radiation but only bremstralung radiation: -4 P = 1.43 1 Z n n T W / m b If there are impurities with high atomic numbers, You have high loss rates due to line radiation can be present. Confinement losses: Plasma energy per unit volume is given by 3 E = k n T + n T c e e i i At the end of the confinement after "energy confinement time of τ c seconds this energy is release, therefore it is lost the loss. The energy lost per unit of time is i c τ c is a confinement cycle depending on the c fusion system (reactor). c 1 P = E e 3 5
Energy balance in CTF Conditions to be reached for CTF : - Ignition: P f, P b + P C - Breakeven: P f P b + P C CTF obtained through DD reactions assuming that: n = n e = n i, T = T e = T i. To have ignitions it is necessary that: 3knT ¼ n v Q + 1.43 1-4 f n T n c ¼ v f c Q 3knT -1.43 1-4 T 11 Energy balance in CTF Schematic of a power plant with a CTF reactor 1 6
Energy balance in CTF Lawson criterion Lawson criterion is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the products of the fusion reactions is sufficient to maintain the temperature of the plasma against all losses without external power input. The criterion gives a minimum required value for the electron density n e and the "energy confinement time c. - Released power after a cycle od a time c : P out P f + P b + P C - Power to be supplied to reach CTF conditions: P in P b + P C If is the CTF conversion efficiency, for the self-maintenance of the process it must be: P out P in CTF obtained through DD reactions with n = n e = n i, T = T e = T i, it is n c ¼ v f Q 3knT -1.43 1 1 - -4 T 13 Energy balance in CTF Criterions for breakeven and ignition (also Lawson criterion ) 14 7
Magnetic confinement The magnetic confinement in CTF is realized by means of magnetic containment of the fusion plasma (T 1 kev) that exploit the property of charged particles that have to move on the walls of magnetic flux tubes. 15 Magnetic confinement Pinch effect + A discharge in a gas induces an azimuth induction field that is composed of the current and produces a centripetal force acting on the charged plasma particles. This phenomenon takes the name of pinch effect. J J B 16 8
Magnetic surfaces The Dall'equazione equation of di the conservazione momentum conservation della quantità equation di moto e and dall'equazione the nd Maxwell di Ampere: law are: p + t u uu JB B J L'equazione At equilibrium di conservazione the equation of della the momentum quantità di conservation moto all'equilibrio equation diviene: becomes: p = JB moltiplicando By means of of scalarmente the multiplication tale equazioneof per this Jequation e per B: by J and B alternatively, it is: J p = B p = J and B lie on isobaric surfaces. 17 Magnetic surfaces in linear configurations For Per linear le scariche configuration nelle configurazioni of the discharge lineari (z-pinch) pinch) the momentum dalla continuità conservation della quantità equation di ismoto: dp dr =-J B dp=-j B dr z z From Dall'equazione the nd Maxwell di Ampere: law it is: l Bdl= I z rb = r J z B = 1 rj z 3 r dp = -½ J r dr z Z-Pinch + Detto For the R external il raggio radius esterno of the della discharge scarica, R p it = is p per = : r = R: R R R dpr = r dp=- rpdr R p R p R R r dp = R p I 8 3 J zr dr J zr 8 z 4 Assuming J z constant. I z B 18 9
Linear configurations Bennet relation From the B = rj z / it is B = I z /R (J z. constant for r R) it follows: B R p I z p 8 If Si N definisce = R n con is the N number = R n of il numero particles di per particelle unit of per length unità di of lunghezza the discharge, della as scarica. p = nk(t Poiché p = nk(t i +T e ) i +T e ), for the z- pinches si ottiene (linear la relazione discharges) Bennet the Bennet per le configurazioni relation follows lineari (z-pinch): as: + Nk T + T i e 8 I z I z For Per un a LTE plasma plasma in ETL where con gas temperatura temerature de and gas electron temperature uguale alla temperatura are equal, the degli Bennet elettroni relation relazione is: di Bennet diviene: Nk T I z 16 B 19 Linear configurations Bennet relation The beta parameter is defined (not to be confused with the Hall parameter) as the ratio between the thermodynamic pressure and the magnetic pressure: p = B / p B = p B / 8 R I z Nk T + T i e I 8 Bennet Relation z + I z B 1
Linear configurations Bennet relation A z-pinch discharge shift causes an increase in B within the discharge column and a decrease in B on the outside. There is therefore a more intense Lorentz force inside than outside causing instability with amplification of the deviation from linear geometry. To stabilize the z-pinch a magnetic induction field B parallel to the axis whose force lines remain within the discharge as B is parallel to J. B forces the charged particles to move along their own flux lines and the discharge does not deviate from the linear geometry. For the z-pinch stabilized Bennet relationship it is: Nk T + T i e 8 I z J + B B J 1 Toroidal configurations To eliminate particle losses in the electrode regions, in parallel to the discharge axis, and energy losses due to the contact with the electrodes, toroidal configurations are used. 11
Toroidal configurations In the inner side of the toroidal configuration, B and the Lorentz's strength are more intense than in the external side. Thus the plasma torus tends to expand. In order to avoid this, a magnetic field parallel to the major axis of the torus, a vertical field B z is added. The component of the poloidal field produced by the plasma current B θ outside the torus is increased and inside of it is is decreased. Thus, a balance effect prevents the torus expansion. In addition a toroidal field, B, is added to have a stable configuration (as in the stabilized z-pinch). B Confining poloidal B B z : Balancing axial B B Stabilizing toroidal B 3 Toroidal configurations Derivation of B z : The forces acting on the radial direction: - F p : due to the thermodynamic pressure; -F m : due to the magnetic pressure depending on W m =½LI (magnetic energy where I is the plasma current); -F z : due to the vertical field B z. From the principle of virtual work : dl p = p dv = p R = a p dr + dr - R a = dl p Fp = = a p = Nk Te T = I f dr 4 Toroidal coordinates: r, 8R Cilindrical coordinates: R, z, d R ln dw a m dl F m = = ½I = ½I = dr dr dr L coefficientediautoinduzi onedelplasma. Per torosottile(r a) 8R = ½I ln 1 8R For thin etorus distribuzi (R a) onedicorrenteuniforme: and J L Rln a a z R R a r 1
Toroidal configurations F p and F m are oriented toward the increasing R-direction (R majour torus radius) therefore act to expand the torus, F z is directed toward the decreasing R- direction : F = R I B z z Hence F z is balancing F p +F m : F+F =F p m z B = I z R ln 8R 1 4 a 5 Toroidal configurations Security factor q The Il passo pitch della of the linea of di the forza spiral del magnetic campo flux magnetico lines is: è: B B pr = r B B The Il fattore security di sicurezza, factor q, funzione function di of r, r, è: is: qr = pr R = r R B B B p Ergodic behaviour of the field linens: q is an irrational number, the field lines lay on the isobaric surfaces and completely cover them. Non-ergodic behaviour of the field linens: q is rational, the field lines after a certain number of turns close on themselves. 6 13
Toroidal configurations B B p p B B Tokamak - Stellarator In tokamaks the plasma is created by the discharge current (plasma current) I and B is induced by I The stability is reached by B In stellarators I and B is induced by external currents. Reversed Field Pinch In RFP the plasma is created by the plasma current I and B is induced by I The stability is reached by B which go to zero and then reverses. 7 Toroidal configurations In a stellarator the plasma current is zero and all fields are produced by external currents. For the solenoidality of B, it is B 1/R. If only B is present, a drift velocity would induce a charge separation and, as consequence, an electric field E. Thus, a drift velocity due to E of the same direction for negative and positive particles is determined. This would produce a torus expansion. A B θ field is required to rotate the positive particles from the bottom up and the negative particles from top to bottom by limiting the effect E. Torus only with B R Torus with B eb v E + E v C v C B B 8 14
Instability in fusion plasmas MHD instability (macroscopic instability): it concerns the location of plasma equilibrium and cause disruption of the discharge following displacements from the equilibrium position. Microscopic instability: they affect transport quantities and cause both particle and energy losses. 9 Instability in fusion plasmas Equilibrium analysis Energy principle: By means of continuity equations and Maxwell's equations, can express the potential energy of the system U (ξ) as a function of the displacement ξ. The equilibrium position is at ξ =. - Stable equilibrium: U (ξ) > U() - Unstable equilibrium: U (ξ) < U() Modal Analysis: Through the MHD model the configuration behaviour for a displacement of ξ with respect to the equilibrium position with ξ =, is studied: = (r) expi[(m n ) ] Depending on the boundary conditions, the instability of poloidal mode are with m =, 1,,... (also called flute or sausage instability, kink or braid instability, second order instability, etc., and the instability of toroidal modes with n =,1,,3... 3 15
Instability in fusion plasmas m = m = 1 m = Poloidal instabilities a. Flute instability (m = ); b. Kink instability (m = 1); c. Second order instability (m = ). Toroidal instabilities 31 Instability in fusion plasmas Instability control in Tokamaks: In order to suppress the instability of the poloidal mode from the mode to the mode m, it needs that: qa = a B m R B From the expression of q(a) and as from the 1 st Maxwell s law (Biot-Savart law) I = ab /, it follows: I < m a B R 3 16
CTF Additional plasma heating P J = EJ = J /: As T 3/, increase with increasing. This is a limit for the Joule heating. Moreover I and J are limited as q(a) > m. In order to control the poloidal mode m of the instability it must be: I a B /(m R ). To increase the temperature additional heating is necessary. This can be done by means of: Adiabatic heating (T/n = const.) Neutral injection Radiofrequency heating (F = 1 MHz 1 GHz) 33 CTF Additional plasma heating Adiabatic heating: T/n = const. 34 17
CTF Additional plasma heating Radiofrequency heating e = eb m e i = eb m i L = pi 1+ pe pi (f 1 GHz) (f 1 MHz) (f 1 GHz) U = pe + e (f 1 GHz) 35 CTF Additional plasma heating Neutral injection A f + A + A f+ + A (Charge exchange) A f + e A f+ + e (Electronic impact ionization) A f + A + A f+ + A + + e (ionic ionization) I(x) = I exp[-x/ ] =1/(Q ionizz n) a/4 (a torus small radius) 36 18
Toroidal machines Tokamak Machines - Transformer effect Air magnetic core Iron magnetic core Tokamak Machines The tokamak machine m requires to have a compact configuration (a R, B θ B Φ affichè I Φ ) qa = a R B B m 19
Tokamak Machines Main windings Tokamak Machines I(B tr ) I(B z )
Tokamak Machines Behaviour of the main currents during a pulse Toroidal field current Primary transformer current Plasma current Tokamak Machines Pl.Maj. rad..935 m Pl. Min. Rad..31 m Pl. Current 1.6 MA Tor. Field 8 T Tor. Field En. 16 MJ Pol. Field En. MJ Pulse Rep. Rate: 1 pulse every min. 1
Main Tokamak Machines T15 JT6 TFTR JET Russia Japan USA UE R [m].43 3..55.96 a [m].7.95.9 1.5 (.1) B [T] 5.5 4.5 5. 3.45 I P [MA].3.7 3. 5.1 JET - Joint European Torus (Culham - GB) Dimensions: R =.96 m, a = 1.5 (.1) m, B = 3.45 T, I φ = 5.1 MA
JET - Joint European Torus (Culham - GB) Electrical power Fusion power [W] Year Remote handling Tokamak Fusion Test Reactor - TFTR Princeton Plasma Physics Laboratory Design Achieved R.1-3.1 m.1-3.1 m Pl.Maj. Rad. a.4-.85 m.4 -.96 m Pl. Min. Rad. B ϕ 5. T 6. T Tor. Field I ϕ 3. MA 3. MA Pl.Current P NBI 33 MW 39.5 MW N. Beam Pow. P ICRF 1.5 MW 11.4 MW ICRF Power 3
Performance Q= P f P IN Q = P f, P IN (where: P IN = P C +P b ) Reversed Field Pinch 4
Reversed Field Pinch RFX Padova Stellarator Continuous regime machine 5
Stellarator Wendelstein Wendelstein 7-X 7-X Max Plank Inst. für Plasmaphysik, Greifswald, Germany Max Plank Inst. für Plasmaphysik, Greifswald, Germany Major radius: 5.5 m Minor radius:.53 m Plasma volume 3 m 3 Non planar coils: 5 Planar coils: Number of ports: 99 Rot. transform: 5/6 5/4 Induction on axis: max. 3T Stored energy: 6 MJ Heating power 15 3 MW Pulse length: 3 min Machine height: 4.5 m Maximal diameter: 16 m Machine mass: 75 t Cold mass: 39 t W7 X symmetry: 5 identical modules Module symmetry: flip symmetrical half 51 Wendelstein 7-X Max Plank Inst. für Plasmaphysik, Greifswald, Germany 5 6
Wendelstein 7-X Vacuum chamber Magnetic System Plasma 53 ITER International Thermonuclear Experimental Reactor Cadarache (Proveza), France Central transformer coils Nb 3 Sn, 6 moduls Toroidal coils Nb 3 Sn, 18 moduls 5,3 T on the plasma axis Poloidal coils Nb-Ti, 6 modules ITER will start in 19. Nel 7 will produce electrical power of 5 MW for about 15 minutes. Criostat 4 m haigth x 8 m diam. Plasma characteristics Majour radius: 6. m Minor average radius: m Volume: 84 m 3 Current: 15 MA Density: 1 m -3 Temperature: 15- kev Fusion power: 5-7 MW Pulse time > 3 s Port Plug Criogenich pumps 8 54 7
ITER Vacuum Chamber and remote handling system 55 ITER Additional heating q Dipartimento di Ingegneria Elettrica 56 8
ITER Magnetic system 57 ITER Estimated cost The estimated cost for construction is 4 6 M (5 value). About 5, M have been estimated for years of operation. Partners' contribution to construction is: o EU: 5% o JA RF CN KO US IN: 1% ciascuno 1% of the total cost is held as a reserve. 58 9
EU Strategy DEMO : To demonstrate electric energy production on a scale of FPP DEMO ITER: Scientic and technological feasibility Fusion Power Plant (FPP): Safe and acceptable for environmental impact and cost 59 Fusion Power Plant (FPP) Breeding Blanket Poloidal Field Coil Toroidal Field Coil Power Conversion System Heating & Current drive D+T+ashes Pumping Supply Electric Power to the Grid Isotope Separation 6 3
Fusion Power Plant (FPP) Safe and environmental impact Radiotoxicity (relative units) Nuclear fission Fusion Ashes of a coal plant Time after the arrest 61 31