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$Studies of fractional D-branes in the gauge/gravity correspondence ...$

1. INTRODUCTIONIn a steady state self sustained fusion plasma the energy input would come fromfusion reactions. The power input is denoted by fusion reactions, P in which measuresthe rate at which fusion energy is deposited in the plasma; it is smaller than the rate offusion energy production, because only the kinetic energy of charged reaction products,such as alpha particles, can be contained. Neutron energy is too quickly lost to thewalls of the containing vessel to contribute to P in . This is due to the fact that theneutrons have no charge and are highly energetic therefore, they rarely react with theplasma particles, hence, their energies are not deposited into the plasma. We expressthe radiation losses by P rad , where the subscript refers to bremsstrahlung radiation.Cyclotron radiation losses are conventionally omitted because their longer wavelengthallows at least partial reflection at the plasma boundary. Thus W in = P in − P rad andfusion plasma power balance is expressed asP in − P rad = U (1.6)τ EIt was noted by Lawson that, while the energy content is proportional to plasmadensity, n, both quantities on the left-hand side of (1.6) vary with the square of thedensity. That P in is proportional to n 2 follows immediately from the binary nature offusion reactions; in a D-T plasma with equal amounts of D and T,P in = 1 4 n2 i 〈σv i 〉E DT (1.7)where E DT = 17.6 MeV is the mean reaction energy of two primary D-T reactions and〈σv i 〉 is the reaction cross-section averaged over the relative velocity of colliding ions.The bremsstrahlung power loss scales asP rad ∝ n 2 eT 1/2e (1.8)It follows that the density enters (1.6) only through the combination nτ E , the Lawsonparameter. For a pulsed reactor with an efficiency of 33% for conversion of heat toelectricity, Lawson gave the criteria both for the minimum temperature and for theminimum (nτ E ) c value at the optimum temperature:T ≥ 3 keV and (nτ E ) c ≥ 10 20 m −3 s at T ≈ 30 keV for D − T (1.9)8
1.7 Plasma Operational LimitsIt is evident that smaller values of nτ E correspond to energy losses too severe forself-sustained fusion; larger values could presumably be cured by artificially enhancedlosses. Thus, the Lawson criterion for self-sustained, or “ignited” fusion, states thatthe product of density and confinement time must equal or exceed (nτ E ) c .The result is sensitive to the particular fusion reaction considered, as well as tovarious plasma parameters (such as impurity content) that are not easy to predict, sothat a simple general specification is difficult.1.7 Plasma Operational LimitsFigure 1.5: Fusion triple product. The figure is taken from Ref. (2).In recent years there has been considerable development of databases and accumulationof knowledge on the behavior of tokamak plasmas around the world. A degreeof uncertainty still exists in predicting the confinement properties and plasma performancein such a device. The progress of these researches can be illustrated by the fusionproduct n DT τ E T i , which represents a figure of merit for plasma performance (see figure9
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4. DRIFT INSTABILITY ANALYSIS: LINE
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9. DISCUSSIONthat the impurity dens
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9. DISCUSSIONthe plasma distributio
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REFERENCES[21] Weiland J. Collectiv
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REFERENCES[73] Neuhauser J. et al.
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PhD and MPhil Thesis Classes - UniversitÃ© Libre de Bruxelles

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