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TMX upgrade magnet system: Design characteristics and physics considerations

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Abstract

Summarized in this article are the design characteristics of the magnet-system configuration constructed for use in the modified Tandem Mirror Experiment (TMX Upgrade), and a description of the resulting vacuum magnetic field. Many engineering and physics considerations and limitations governed the design. Several of the physics issues are discussed here, including single-particle drift surfaces and adiabaticity, central-cell resonant radial transport, magnetohydrodynamic stability analysis, and finite-beta equilibrium. The described design procedures can be applied to other tandem-mirror experiments or reactor studies.

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Abbreviations

a :

radial-displacement parameter (or reflection function), cm

B :

magnetic-field vector,T

¦B¦ orB :

magnetic-field magnitude, T (or G)

D 0,D 1 :

resonant-radial-transport diffusion coefficients, cm2/s

E :

electric-field vector, kV/m

L :

end points (±) of the machine, whereP ∥ vanishes, m

L s :

effective length of the solenoidal central cell, used in the radial-diffusion-coefficient calculations, m

n :

plasma species density, cm−3

P :

plasma-particle pressure (often written equal tonkT, wherek is the Boltzmann constant andT here is in K), erg/cm3

P :

B-dependent part of plasma-particle pressure when written in separable form, erg/cm3

q :

elementary charge

r :

radius in cylindrical-coordinate system, cm or m

r c :

central-cell plasma radius, cm

R eff :

effective radial scale length for estimating central-cell gradients, cm

R eff :

ratio of maximum-to-minimum magneticfield magnitude experienced by a trapped particle during its motion

T :

particle energy or “temperature,” keV or ergs

T φ :

an effective energy used for calculating central-cell potential gradients, keV

gv :

particle velocity, cm/s

W :

particle kinetic energy, keV

x, y, z :

Cartesian coordinates, cm or m

α:

azimuthal angular coordinate (Sections 5 and 6 only), deg

β :

the plasma “beta” in this article, where β ≡ β⊥ =8πP ⊥ /B 2, the ratio of the plasma-particle perpendicular pressure (P ⊥ ) to the pressure of the confining vacuum magnetic field (B2/8π)

β p ,β c :

beta values at the center of the end and central cells, respectively

ɛ:

ion kinetic plus potential energy, keV

θ :

pitch angle, the angle between the particle velocity vector and the magnetic-field direction, deg

θ inj, θ lc :

pitch angles at the end-cell midplane of the injected particles and of the loss cone, rad

κ:

magnetic-field-line curvature vector, cm−1

κgy, κα :

components of κ, with dimensions cm−2. T−1 and rad−1, respectively

μ :

particle magnetic moment, keV/T

vψ,v z :

azimuthal-precession and axial-reflection (one cycle includes a bounce at each end of the confining cell) frequencies, kHzv(ψ)ψ-dependent part of plasma-particle pressure when written in separable form (Sections 5 and 6 only)

τ ad :

adiabatic lifetime, s

τ1, τ2 :

resonant-radial-transport diffusion lifetimes, ms

ψ(r) :

electric potential at the central-cell midplane, relative to ground, kV

ψ e :

ψ(r) atr=0, kV

ψ:

used in two different ways: (1) polar angular coordinate in cylindrical-coordinate system, deg; (2) principal flux coordinate (Sections 5 and 6 only), cm2 · T

ω :

eigenfrequency or growth rate for ballooning instability mode, rad/s

c :

central cell

e :

electron plasma species

i :

ion plasma species

p :

end cell (or “plug”)

⊥, ∥:

referenced to the magnetic-field direction

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Authors and Affiliations

  1. Lawrence Livermore National Laboratory, University of California, 94550, Livermore, California

    J. H. Foote, A. K. Chargin, R. H. Cohen, T. B. Kaiser, C. V. Karmendy, T. C. Simonen & R. L. Wong

Authors
  1. J. H. Foote
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  2. A. K. Chargin
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  3. R. H. Cohen
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  4. T. B. Kaiser
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  5. C. V. Karmendy
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  6. T. C. Simonen
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  7. R. L. Wong
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Additional information

C. V. Karmendy is deceased.

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Foote, J.H., Chargin, A.K., Cohen, R.H. et al. TMX upgrade magnet system: Design characteristics and physics considerations. J Fusion Energ 2, 383–402 (1982). https://doi.org/10.1007/BF01053133

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