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Conception of divertorless tokamak reactor with turbulent plasma blanket
CONCKPTION OF DIVRRTORLRSS TOKAMAK REACTOR WITH TURBULENT PLASMA BLANKET A.V. NEDOSPASOV and M.Z. TOKAR Instih&of High Temperaturesof the USSR Academy of Sciences, Moscow, USSR
1. Introllllction The increase in the plasma diffusion in the region near the wall of a tokamak reactor can be an effective way of increasing the neutral atom recycling of helium and unburned fuel exhaust. It also reduces the energy of the particles interacting with the wall. This phenomenon can be explained with the following simple reasoning. The heat from the plasma is transferred to the wall (r = a) by convection, and we obtain the estimate:
40-r - TI,,.
=-TD$dr
Here k is the sum of the charge-exchange and ionization constant and ff is the mean plasma density in the region near the wall. Consequently:
46
, -Di2; D fA"k'm.
r(a)-
D$i4k2m. 4. I-D:.
&=&exp(-l--&)$(1+&
(1)
I ,zo’
where q. is the heat flux from the active zone of the reactor. With recycling the mean scale of the plasma density change is determined by the penetration length of the fast neutral atoms (lo):
T(a) -
The stochastisation of magnetic field lines by the external helical windings is a possible way to increase D&z). In the case where the electric current flows along the closed windings, doing m rounds along the torus and I rounds across it, the family of magnetic islands arises instead of the magnetic surface with q, = m/l. Overlapping of the islands leads to a magnetic field lines stochastisation and an increase of the transversal diffusion [6]. According to [7]:
These estimates have been confirmed by the detailed calculations on the basis of the Bohm [l] and pseudoclassic [2] transport coefficients in the neanvall region. An increase of the transport coefficients can be induced by instability. For example, the plasma blanket with helical (current-convective) instability was discussed in ref. [3] (see also [4,5]).
where E = a/R, R is the major torus radius, Jo is the plasma current, J1 is the winding current, V, is the speed of sound, and S is the dimensions of the stochastisation zone. The number of windings no is equal to a/m& The resonant magnetic surface coincides with the first wall if the stochastic@ system windings is placed at a distance 2a :JI/Jo * =
46
[l + (2ahr) (J1/Jo)1n]2E
(2)
behind the first wall. 2. The physical model and the system of equations The plasma is described by the system of MHD equations and the behaviour of the fuel neutrals (D, T) is described by the kinetic equation [8] v, E=
-knf. + k,n,f,
Journal of Nuclear Materials 93 & 94 (1980) 248-251 @ North-Holland Publishing Ciwapany
(3)
248
A.V. Nabspasm, M.Z. Tokar / Cbnception of divertorkss tokamak
where k, is the charge-exchange constant, x = a - r, and A fi are the velocity distribution functions for atoms and ions, respectively. The mean energy of the atoms desorbed from the wall is equal to &- fT(a)R&, where R, and RE are the particle and energy reflection coefficients. With a stainless steel surface these coefficients for hydrogen and helium are close to 0.7 [9]. An analytic solution of eq. (3) has been obtained in the literature [lo] and it is valid if the plasma temperature change in the nearwall region is much less than the plasma density change. The behaviour of helium atoms is described in the “r-approximation” by the equation analogous to eq. (3): V’ %
= -(kl + kz + &k$tfHe
+ n4ondkz
+
k& ).
(4)
Here kl is the helium atoms ionisation constant, k2 is the mean constant of the He atoms elastic scattering on deuterium and tritium ions, k3 is the total constant of collisions between helium atoms and ions, & is the ratio of the helium and fuel density, and 40 is the velocity part of the helium ion distribution function. The chargeexchange of He neutrals on He+ particles and elastic scattering on D+ and T+ ions build up recycling of the helium atoms in the region near the wall. 3. The caleulatfons for INTOR The analytic equations has assumption that diffusion in the given by:
solution of the system of the been obtained* under the “PLT-scaling” for the plasma central zone of the tokamak is
D, = [1+ 9(r/a y] x 103cm2/s. Near the wall D,(u) = D, + 104cm2/s. The reactor parameters have been taken as follows: q. = 40 W/cm2, the mean plasma density in the reactor n’ = 1.2 x 10” cm-‘; lo = 6 Ma; B = 5 T; a = 1.5 m; the ellipticity b/a = 1.5; R = 5 m; S = 1Ocm; q(a)= 2.5; m =5; 1= 2. The a-particle outihtx from the active reactor zone Pg is l
To be published in Fiz. Plazmy, USSR.
249
equal to 7 x 1013cmS2 s-r. The unburned fuel out&x PO is “a free parameter” depending on the fuel injection beyond the combustion. The constants of the elementary processes have been taken from [ll, 121: ki z k,,
12.5 X lo-*
Cm3/S;
kl 1:
1.5 x 10” cm3/s,
k2 =
3.5 x lo+’ cm3/s,
k3 =
1.4 x lo+’ cm3/s.
We assume that some portion of the D, T neutrals can leave the chamber through holes in the wall and then may be absorbed in cryopanels, for instance. For the helium exhaust the vacuum pumps may be used. In the pump vessel helium atoms will become cold, and their equilibrium density may be calculated according to the equality of the helium fluxes to the pump and back to the reactor:
Here V& is the helium thermal velocity at room temperature. Fig. 1 demonstrates the I’& and nj& dependence on the diffusion constant D,(u). The ratio of the total area of the wall holes to the first wall area surface is given by rt/I’& and is presented on the right scale. The necessary pump rate may be estimated by +P:.s nB ’ where S is the total area of the first wall. The dependence of the diffusion constant D(u) on the total winding current Z J1 is presented in fig. 2. With the unburned fuel flux PO= 2 x 1Ol5 cm-‘ s-’ and X JI = 0.85 MA, nL = 1.2 X lOI cmv3, and e = 2.3 x 10s 1s-l. This pump rate requires 23 pumps each pumping 1041s-l. At the tokamak axis & is equal to lo-15% (see fig. 3) and T(a) = 17 eV. With the water-cooled copper windings and the winding current density being equal to 2 l&/cm2 the total winding cross-section is equal to 425 cm2. From the neutron penetration standpoint this corresponds to a sufficiently thin effective copper layer of 0.35 cm.
A.V. Nedospasov, M.Z. Tokar I Conceptionof divertorlesstokamak
250
4(a)
-
Fig. 1. The dependence of l&, diffusion constant D&x).
DL (a)
HO4cm2 s-9 n$,
on the
[104cm2 5’1 5
t
I
and rg/&
-
r. IIO~~C&S-~I Fig. 3. The dependence of &(O) on ro. ro is the radius of the active zone of the reactor.
r = 10'6cm-2 $1
1 4
7.10'5
3
4.l0'5 -2.1015
2
'$15
1 P
“-
-
EJ1CMAI
Fig. 2. The dependence of DJa) on the total winding current Z 51.
The sputtered impurity atom fhrx from the first wall is
Here I= ~2~l(a)V$~$‘(l - AH)& and KY and V$’are the ionisation constant and the mean velocity of impurities. According to (6) a long way from the wall (x is much more than the impurity ionisation length I) III 5 6 x 10” cm-‘. It has been taken into account in this estimate that the mean energy of neutrals sputtering the wall is more than @(a) and their distribution function is distinct from the Maxwellian one. The sputtering coefficients were taken from ref. [15].
(5) where S@), W), and S(I-Ie) are the velocityaveraged sputtering coefficients for deuterium, tritium, and helium atoms, respectively, and I’, is the sum of D, T neutral flux from the wall. The behaviour of the impurity is treated under the assumption that the diffusion constant is the same for all kinds of ions. The impurity density in the nearwall region is described by [13,14] x/l
nl =
r11
s
I 0
e-" dt.
4. conchl!&uls The results of the calculations presented here demonstrate that, with technically reasonable degree of the magnetic field stochastisation, the turbulent plasma blanket can take the place of a divertor. It performs the three main functions of the divertor: (a) the exhaust of the helium and unburned fuel; (b) weakening of the fast particle flux to the wall surface; and
A.V. Nedospasov, M.Z. Tokar / Conception of divertorless tokamak
(c) essential reduction of the impurity content in the active zone of the reactor. Taking into account that plasma flows to the first wall along field lines, we may figuratively say that the first wall plays the role of a divertor in our conception. Our estimates show that the neoclassical impurity particles transported under the conditions of the magnetic field lines stochastisation do not result in any essential accumulation of the impurities in the reactor volume. The impurity density is much less than critical for thermonuclear burning (nr s 1On cm-‘). The method of the processes of generation in the near-wall region considered in the present paper gives a flatter profile of the plasma density in the tokamak reactor than in the divertor case. It must improve the utilisation of the apparatus volume and fuel injection. The control of transport processes on the plasma surface can be a new way for regulating the reactor action. Certainly, only experimental testing of the ideas suggested, and more detailed technical elaboration, will allow us to appreciate its capacity for competing with a divertor.
251
References [l] N.N. Vasilyev, A.V. Nedospasov, V.G. Petrov and M.Z. Tokar, At. Energy 44 (1978) 336. [2] V.G. Petrov and M.Z. Tokar, Fii. Plazmy 4 (1978) 822. [3] A.V. Nedospasov, in: Proc. 7th Europ. Conf. on Contr. Fus. and Plasma Phys., Laussanne, Vol. 1 (1975) p. 129. [4] D.K. Bhadra and L. Gross, Nucl. Fusion 17 (1977) 622. [5] D. Anderson, M. Lisak and H. Wilhelmsson, Nucl. Fusion 19 (1979) 1522. [6] W. Feneberg, in: Proc. 8th Europ. Conf. on Controlled Fusion and Plasma Physics, Prague, Vol. 1 (1977) p. 4. [7] M.Z. Tokar, Fii. Plaxmy 5 (1979) 454. [8] S. Rehker and H. Wobig, Plasma Phys. 15 (1973) 1083. [9] O.S. Oen and M.T. Robinson, Nucl. Instr. Methods 132 (1976) 1083. [lo] D.N. Zubarev and V.N. Klimov, in: Fiika plaxmy i problema upravliyemyh termoiydemyh reakcij, Vol. 1 (AC. SC. of USSR, Moscow, 1958) p. 138. [ll] L.A. Vainshtein et al., Secheniya vozbuzhdeniya atomov i ionov electronami (Atomizdat, Moscow, 1973). [12] E.W. McDaniel, Collision Phenomena in Ionized Gases (New York, 1964). [13] A.V. Nedospasov and M.Z. Tokar, Rep. IVTAN, 744, Moscow (1979). [14] W. Engelhardt and W. Feneberg, J. Nucl. Mater. 76/77 (1978) 518. [15] J. Roth, J. Bohdansky and W. Ottenberger, MaxPlanck-Institut fur Plasmaphysik, Garching bei Munthen, 1979, IPP 9/26.
1. Introllllction The increase in the plasma diffusion in the region near the wall of a tokamak reactor can be an effective way of increasing the neutral atom recycling of helium and unburned fuel exhaust. It also reduces the energy of the particles interacting with the wall. This phenomenon can be explained with the following simple reasoning. The heat from the plasma is transferred to the wall (r = a) by convection, and we obtain the estimate:
40-r - TI,,.
=-TD$dr
Here k is the sum of the charge-exchange and ionization constant and ff is the mean plasma density in the region near the wall. Consequently:
46
, -Di2; D fA"k'm.
r(a)-
D$i4k2m. 4. I-D:.
&=&exp(-l--&)$(1+&
(1)
I ,zo’
where q. is the heat flux from the active zone of the reactor. With recycling the mean scale of the plasma density change is determined by the penetration length of the fast neutral atoms (lo):
T(a) -
The stochastisation of magnetic field lines by the external helical windings is a possible way to increase D&z). In the case where the electric current flows along the closed windings, doing m rounds along the torus and I rounds across it, the family of magnetic islands arises instead of the magnetic surface with q, = m/l. Overlapping of the islands leads to a magnetic field lines stochastisation and an increase of the transversal diffusion [6]. According to [7]:
These estimates have been confirmed by the detailed calculations on the basis of the Bohm [l] and pseudoclassic [2] transport coefficients in the neanvall region. An increase of the transport coefficients can be induced by instability. For example, the plasma blanket with helical (current-convective) instability was discussed in ref. [3] (see also [4,5]).
where E = a/R, R is the major torus radius, Jo is the plasma current, J1 is the winding current, V, is the speed of sound, and S is the dimensions of the stochastisation zone. The number of windings no is equal to a/m& The resonant magnetic surface coincides with the first wall if the stochastic@ system windings is placed at a distance 2a :JI/Jo * =
46
[l + (2ahr) (J1/Jo)1n]2E
(2)
behind the first wall. 2. The physical model and the system of equations The plasma is described by the system of MHD equations and the behaviour of the fuel neutrals (D, T) is described by the kinetic equation [8] v, E=
-knf. + k,n,f,
Journal of Nuclear Materials 93 & 94 (1980) 248-251 @ North-Holland Publishing Ciwapany
(3)
248
A.V. Nabspasm, M.Z. Tokar / Cbnception of divertorkss tokamak
where k, is the charge-exchange constant, x = a - r, and A fi are the velocity distribution functions for atoms and ions, respectively. The mean energy of the atoms desorbed from the wall is equal to &- fT(a)R&, where R, and RE are the particle and energy reflection coefficients. With a stainless steel surface these coefficients for hydrogen and helium are close to 0.7 [9]. An analytic solution of eq. (3) has been obtained in the literature [lo] and it is valid if the plasma temperature change in the nearwall region is much less than the plasma density change. The behaviour of helium atoms is described in the “r-approximation” by the equation analogous to eq. (3): V’ %
= -(kl + kz + &k$tfHe
+ n4ondkz
+
k& ).
(4)
Here kl is the helium atoms ionisation constant, k2 is the mean constant of the He atoms elastic scattering on deuterium and tritium ions, k3 is the total constant of collisions between helium atoms and ions, & is the ratio of the helium and fuel density, and 40 is the velocity part of the helium ion distribution function. The chargeexchange of He neutrals on He+ particles and elastic scattering on D+ and T+ ions build up recycling of the helium atoms in the region near the wall. 3. The caleulatfons for INTOR The analytic equations has assumption that diffusion in the given by:
solution of the system of the been obtained* under the “PLT-scaling” for the plasma central zone of the tokamak is
D, = [1+ 9(r/a y] x 103cm2/s. Near the wall D,(u) = D, + 104cm2/s. The reactor parameters have been taken as follows: q. = 40 W/cm2, the mean plasma density in the reactor n’ = 1.2 x 10” cm-‘; lo = 6 Ma; B = 5 T; a = 1.5 m; the ellipticity b/a = 1.5; R = 5 m; S = 1Ocm; q(a)= 2.5; m =5; 1= 2. The a-particle outihtx from the active reactor zone Pg is l
To be published in Fiz. Plazmy, USSR.
249
equal to 7 x 1013cmS2 s-r. The unburned fuel out&x PO is “a free parameter” depending on the fuel injection beyond the combustion. The constants of the elementary processes have been taken from [ll, 121: ki z k,,
12.5 X lo-*
Cm3/S;
kl 1:
1.5 x 10” cm3/s,
k2 =
3.5 x lo+’ cm3/s,
k3 =
1.4 x lo+’ cm3/s.
We assume that some portion of the D, T neutrals can leave the chamber through holes in the wall and then may be absorbed in cryopanels, for instance. For the helium exhaust the vacuum pumps may be used. In the pump vessel helium atoms will become cold, and their equilibrium density may be calculated according to the equality of the helium fluxes to the pump and back to the reactor:
Here V& is the helium thermal velocity at room temperature. Fig. 1 demonstrates the I’& and nj& dependence on the diffusion constant D,(u). The ratio of the total area of the wall holes to the first wall area surface is given by rt/I’& and is presented on the right scale. The necessary pump rate may be estimated by +P:.s nB ’ where S is the total area of the first wall. The dependence of the diffusion constant D(u) on the total winding current Z J1 is presented in fig. 2. With the unburned fuel flux PO= 2 x 1Ol5 cm-‘ s-’ and X JI = 0.85 MA, nL = 1.2 X lOI cmv3, and e = 2.3 x 10s 1s-l. This pump rate requires 23 pumps each pumping 1041s-l. At the tokamak axis & is equal to lo-15% (see fig. 3) and T(a) = 17 eV. With the water-cooled copper windings and the winding current density being equal to 2 l&/cm2 the total winding cross-section is equal to 425 cm2. From the neutron penetration standpoint this corresponds to a sufficiently thin effective copper layer of 0.35 cm.
A.V. Nedospasov, M.Z. Tokar I Conceptionof divertorlesstokamak
250
4(a)
-
Fig. 1. The dependence of l&, diffusion constant D&x).
DL (a)
HO4cm2 s-9 n$,
on the
[104cm2 5’1 5
t
I
and rg/&
-
r. IIO~~C&S-~I Fig. 3. The dependence of &(O) on ro. ro is the radius of the active zone of the reactor.
r = 10'6cm-2 $1
1 4
7.10'5
3
4.l0'5 -2.1015
2
'$15
1 P
“-
-
EJ1CMAI
Fig. 2. The dependence of DJa) on the total winding current Z 51.
The sputtered impurity atom fhrx from the first wall is
Here I= ~2~l(a)V$~$‘(l - AH)& and KY and V$’are the ionisation constant and the mean velocity of impurities. According to (6) a long way from the wall (x is much more than the impurity ionisation length I) III 5 6 x 10” cm-‘. It has been taken into account in this estimate that the mean energy of neutrals sputtering the wall is more than @(a) and their distribution function is distinct from the Maxwellian one. The sputtering coefficients were taken from ref. [15].
(5) where S@), W), and S(I-Ie) are the velocityaveraged sputtering coefficients for deuterium, tritium, and helium atoms, respectively, and I’, is the sum of D, T neutral flux from the wall. The behaviour of the impurity is treated under the assumption that the diffusion constant is the same for all kinds of ions. The impurity density in the nearwall region is described by [13,14] x/l
nl =
r11
s
I 0
e-" dt.
4. conchl!&uls The results of the calculations presented here demonstrate that, with technically reasonable degree of the magnetic field stochastisation, the turbulent plasma blanket can take the place of a divertor. It performs the three main functions of the divertor: (a) the exhaust of the helium and unburned fuel; (b) weakening of the fast particle flux to the wall surface; and
A.V. Nedospasov, M.Z. Tokar / Conception of divertorless tokamak
(c) essential reduction of the impurity content in the active zone of the reactor. Taking into account that plasma flows to the first wall along field lines, we may figuratively say that the first wall plays the role of a divertor in our conception. Our estimates show that the neoclassical impurity particles transported under the conditions of the magnetic field lines stochastisation do not result in any essential accumulation of the impurities in the reactor volume. The impurity density is much less than critical for thermonuclear burning (nr s 1On cm-‘). The method of the processes of generation in the near-wall region considered in the present paper gives a flatter profile of the plasma density in the tokamak reactor than in the divertor case. It must improve the utilisation of the apparatus volume and fuel injection. The control of transport processes on the plasma surface can be a new way for regulating the reactor action. Certainly, only experimental testing of the ideas suggested, and more detailed technical elaboration, will allow us to appreciate its capacity for competing with a divertor.
251
References [l] N.N. Vasilyev, A.V. Nedospasov, V.G. Petrov and M.Z. Tokar, At. Energy 44 (1978) 336. [2] V.G. Petrov and M.Z. Tokar, Fii. Plazmy 4 (1978) 822. [3] A.V. Nedospasov, in: Proc. 7th Europ. Conf. on Contr. Fus. and Plasma Phys., Laussanne, Vol. 1 (1975) p. 129. [4] D.K. Bhadra and L. Gross, Nucl. Fusion 17 (1977) 622. [5] D. Anderson, M. Lisak and H. Wilhelmsson, Nucl. Fusion 19 (1979) 1522. [6] W. Feneberg, in: Proc. 8th Europ. Conf. on Controlled Fusion and Plasma Physics, Prague, Vol. 1 (1977) p. 4. [7] M.Z. Tokar, Fii. Plaxmy 5 (1979) 454. [8] S. Rehker and H. Wobig, Plasma Phys. 15 (1973) 1083. [9] O.S. Oen and M.T. Robinson, Nucl. Instr. Methods 132 (1976) 1083. [lo] D.N. Zubarev and V.N. Klimov, in: Fiika plaxmy i problema upravliyemyh termoiydemyh reakcij, Vol. 1 (AC. SC. of USSR, Moscow, 1958) p. 138. [ll] L.A. Vainshtein et al., Secheniya vozbuzhdeniya atomov i ionov electronami (Atomizdat, Moscow, 1973). [12] E.W. McDaniel, Collision Phenomena in Ionized Gases (New York, 1964). [13] A.V. Nedospasov and M.Z. Tokar, Rep. IVTAN, 744, Moscow (1979). [14] W. Engelhardt and W. Feneberg, J. Nucl. Mater. 76/77 (1978) 518. [15] J. Roth, J. Bohdansky and W. Ottenberger, MaxPlanck-Institut fur Plasmaphysik, Garching bei Munthen, 1979, IPP 9/26.