An Assessment of the Power Balance in Fusion Reactors
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AN ASSESSMENT OF THE POWER BALANCE IN FUSION REACTORS Masao Nozawa Don Steiner IGSSU OAK RIDGE NATIONAL LABORATORY OPERATED BY UNION CAJ^DE CORPORATION, • FOR THE U.S. ATOMIC ENERGY COMMISSION 0RNL-TM-M21 Contract No. W-7^05-eng-26 Thermonuclear Division AN ASSESSMENT OF THE POWER BALANCE IN FUSION REACTORS Masao Nozawa and Don Steiner [To "be submitted for publication in Nuclear Fusion] JANUARY 1974 OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37830 operated by UNION CARBIDE CORPORATION for the U.S. ATOMIC ENERGY COMMISSION -NOTICE- This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, com- pleteness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights. set _ lEHfi fefe ill AN ASSESSMENT OF THE POWER BALANCE IN FUSION REACTORS* + Masao Nozawa and Don Steiner Oak Ridge National Laboratory, Oak Ridge, Tennessee 3T830 ABSTRACT A general formalism has been developed for analysis of the energy balance in fusion reactors. This formalism has been applied in a detailed and consistent fashion to four current D-T fusion reactor concepts, the laser fusion, the mirror, the thet.a pinch and the tokamak reactor concept. On the basis of a critical examination of the reactor subsystems, sets of reference parameters were adopted for each concept. The plasma performance was cast in terms of an energy multiplication factor, Q, defined as the ratio of the fusion produced energy (including blanket energy release) to the plasma energy at ignition. The Lawson number, ni, and the fractional burnup, f^, associated with a given Q were derived on the basis of assumed values for the plasma ignition and burning temperatures. The values of Q, nx and f required for power break-even ani for net-power production at a given value of the overall plant efficiency, n, were then calculated for each concept using the reference parameters. The sensitivity of the required Q, values to variations from the reference points was examined extensively. The plant energy handling requirements were characterized by two parameters which are useful criteria in economics assessments; the ratio of the supply energy to the net-output energy, S, and the ratio _ Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. t Visiting Scientist from the Japan Atomic Energy Research Institutet Tokai, Ibaraki, Japan. LANbnillKl PAI Mm\Gm ill of the circulating energy to the net-output energy, C. The behavior cf S and C was examined for each concept. AN ASSESSMENT OF THE POWER BALANCE IN FUSION REACTORS* f Masao Nozawa and Don Steiner 1. INTRODUCTION In contrast to fission power reactors, fusion power reactors will inherently require initial heating energy to raise the fuel temperature to the point at which an appreciable amount of nuclear energy is released. Thus, fusion reactors can be viewed as energy multiplying devices. This fundamental aspect of fusion reactors was first quantified by J. D. Lawson [l] who formulated a convenient expression for the plasma parameters, n (density) and T (confinement time), required for fusion power break-even. The product, nx, is often referred to as the Lawson number and is ussd as a figure of merit in assessing plasma performance. Previous examinations of power balances in fusion reactors can be classified into two categories: (l) specific studies [2-5] and (2) general studies [1,6]. The specific studies focus in detail on the power balance of a particular reactor concept. Since the various specific studies have not been carried out on a common basis, it is difficult to compare the results obtained for different reactor concepts. The general studies focus on the formulation of the power balance equations. However, once developed, these equations are not applied to the various reactor concepts in a detailed fashion. The purpose of the present work is to combine Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. t Visiting Scientist from the Japan Atomic Energy Research Institute, Tokai, Ibaraki, Japan. 2 the specific and general approaches in order to critically investigate power balances in fusion reactors on a common basis. The basic formulae of the fusion power balance are developed and discussed in Section 2. Using this formalism the requirements and implications of the power balance in current conceptual fusion reactors are examined in detail. The laser-ignited, mirror, theta-pinch and tokamak fusion reactors are investigated in Sections 3, 5 and 6, respectively. The various reactor concepts are compared in Section 7 on the basis of required plasma properties for power break-even and for net power production. 2. GENERAL CONSIDERATIONS 2.1. THE POWER BALANCE EQUATION Consider the hypothetical fusion reactor power plant shown schematically in Figs. 1A and IB. Assuming a pulsed mode of operation, the energy balance equation for the plant may be written in the following general form. W = W Eri,{aQri + fcn + mFn + 6(l-n )} n s d a a a a + W Eri,{(l-a)Qn + + (l-m)Fn + (l-5)(l-n )> (l) s ox a a a a + + W EF <1/ 1) W (1+a) WsEnt2(l/Vl) s Vt3 V - s > where is the net electrical output energy from the plant and Wg is the sum of the electrical energies to the plasma heating subs/stem and the pulsed magnetic field supply subsystem. Thus, W. W W « JL * (2) S n m^ 3 where W^ is the heating energy to the plasma produced with efficiency H and W is the pulsed magnetic field energy produced with efficiency n . nu m m The quantity E is the fraction of W which appears as heating energy to s the plasma and is given by Vm E = n + Fn T\. • (3) m a h where F is the ratio of the pulsed magnetic field energy, W , to the m plasma energy, W , and n is the efficiency with which the heating energy P a to the plasma is absorbed by the plasma. Thus W r = <w P and na = (5) Equation (2) can be rewritten as follows using equations (U) and (5), W = — + —. (6) s n. n h m Therefore, n, n W. = W S-S- = w E (7) h s rj + Fn n, S m an In this study Q is defined as, Fusion energy produced in the plasma and blanket Q = . (8) Heating energy absorbed by the plasma If Wf is the fusion energy produced in the plasma and blanket, then £q. (8) can be rewritten as, Wf p u The first term of Eq. (l) represents the energy recovered by direct conversion with efficiency ri . The symbols a, it, m and 6 indicate portions d of energies recovered by direct conversion and correspond to the fusion energy produced, the plasma energy supplied, the pulsed magnetic energy supplied and the heating energy not absorbed by the plasma, respectively. The second term in Eq. (l) represents the energy recovered by the main thermal converter with efficiency The third term represents heat loss recovered from the plasma heating subsystem by a secondary thermal converter with efficiency Tl^g* term represents heat loss recovered from the pulsed magnetic field supply subsystem by a thermal converter with efficiency H^g* This term, however, will be neglected in the following discussion. The last term in Eq. (l) represents the total input energy to the plasma heating subsystem, pulsed magnetic field supply subsystem, and auxiliary system as shown in Figs. 1A and IB. The factor a in this term indicates the portion of energy consumption due to the auxiliary system in relation to W . The auxiliary system allows for S requirements such as refrigeration and vacuum pumping which consume a continuous power designated by P£ L. If the repetition rate for pulsed operation is f(number of cycles/sec), then the relations between energies and powers are, P (10) n P n (11) and P afW a s (12) In the case of steedy state operation of the fusion reactor, the energy "balance equation can he obtained from Eq. (l) by replacing each- energy term, W^, by a corresponding power term, P^. For steady state operation the definition of Q becomes, Rate of fusion energy produced Q = . (13) Rate of heating energy trapped by plasma All other quantities remain as defined for pulsed operation. When W^ in Eq. (l) is set equal to zero, the equation defines a "critical" value for Q which we shall designate "Qc". The expression for Q is c Q• c = r - ndu+nn) - + F(1-ra)} e a (lb) a an where s ar + e Ud (l-a)n+t1 l • (15) The fusion energy is converted into electricity with efficiency n which will be referred to as the effective conversion efficiency of fusion energy. Equation (lU) shows that Q is a function of the various subsystem * efficiencies. If all the efficiencies were unity, then Qc would equal zero. By combining Eq. (1*0 with Eq. (l), W^ can be expressed as, w = (Q - Q )En n W . (16) n c a e s This shows that the net output energy is proportional to (Q-Q ), E, r) c a and n . The term Q Er| n W corresponds to the energy necessary to 6 C QL 6 S sustain the power plant without production of net output energy.