P/377 USA
`
`Summary of UCRL Pyrotron (Mirror Machine) Program*
`
`By R. F. Post*
`
`Under the sponsorship of the Atomic Energy Com-
`mission, work has been going forward at the University
`of California Radiation Laboratory since 1952 to
`investigate the application of the so-called " magnetic
`mirror " effect to the creation and confinement of a
`high temperature plasma. By the middle of 1953
`several specific ways by which this principle could be
`applied to the problem had been conceived and
`into a proposed
`integrated
`analyzed and were
`approach which has come to be dubbed "The Mirror
`Machine".' Study of the various aspects of the physics
`ot the Mirror Machine has been the responsibility of a
`group
`(called
`the
`Laboratory
`experimental
`"Pvrotron" Group) under the scientific direction of
`the author. During the intervening years of effort,
`experiments have been performed which demonstrate
`the confinement properties of the Mirror Machine
`geometry and confirm several of its basic principles of
`operation. There remain, however, many basic quan-
`titative and practical questions to be answered before
`fusion
`the possibility of producing self-sustained
`reactions in a Mirror Machine could be properly
`assessed. Nevertheless, the experimental and theoreti-
`cal investigations to date have amply demonstrated
`the usefulness of the mirror principle in the experi-
`mental study of magnetically confined plasmas. This
`report presents some of the theory of operation of the
`Mirror Machine, and summarizes the experimental
`work which has been carried out.
`
`PRINCIPLE OF THE MAGNETIC MIRROR
`The modus operandi of the Mirror Machine is to
`create, heat and control a high temperature plasma by
`means of externally generated magnetic fields. The
`magnetic mirror principle is an essential element, not
`only in the confinement, but in the various mani-
`pulations which are performed in order to create and
`to heat the plasma.
`
`Confinement
`The magnetic mirror principle is an old one in the
`realm of charged particle dynamics. It is encountered
`for example, in the reflection of charged cosmic ray
`particles by the earth's magnetic field. As here to be
`
`* Radiation Laboratory, University of California, Liver-
`more, California.
`
`understood, the magnetic mirror effect arises when-
`ever a charged particle moves into a region of magnetic
`field where the strength of the field increases in a
`direction parallel to the local direction of the field lines,
`toward
`lines of force converge
`i.e., wherever the
`each other. Such regions of converging field lines tend
`to reflect charged particles, that is, they are " mag-
`netic mirrors ". The basic confinement geometry of
`the Mirror Machine thus is formed by a cage of
`magnetic field lines lying between two mirrors, so that
`configuration of magnetic lines resembles a two-ended
`wine bottle, with the ends of the bottle defining the
`mirror regions. This is illustrated in Fig. 1, which also
`shows schematically the location of the external coils
`which produce the confining fields. The central, uni-
`form field, region can in principle be of arbitrary
`length, as dictated by experimental convenience or
`other considerations. For various reasons, it has been
`found highly desirable to maintain axial symmetry in
`the fields, although the general principle of particle
`confinement by mirrors does not require this.
`The confinement of a plasma between magnetic
`mirrors can be understood in terms of an individual
`particle picture. The conditions which determine the
`binding of individual particles between magnetic
`mirrors can be obtained through the use of certain
`the
`invariants applying generally
`to
`adiabatic
`motion of charged particles in a magnetic field.
`The first of these invariants is the magnetic mo-
`ment, it, associated with the rotational component of
`motion of a charged particle as it carries out its
`helical motion in the magnetic field. 2 The assumption
`that u is an absolute constant of the motion is not
`strictly valid, but, as later noted, it represents a very
`good approximation in nearly all cases of practical
`interest in the Mirror Machine.
`The magnitude of j is given by the expression
`
`= W 1 /H = mv_1
`
`2/H ergs/gauss
`
`which states that the ratio of rotational energy to
`magnetic field remains a constant at any point along
`the helical trajectory of the charged particle. In this
`case the magnetic field is to be evaluated at the line of
`force on which the guiding center of the particle is
`moving.
`Now, at the point at which a particle moving toward
`a magnetic mirror is reflected, its entire energy of
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`
`plasma by mirrors can be obtained by manipulation of
`the reflection condition. By differentiation, holding
`the total particle energy constant, it can be shown
`that a particle moving along a magnetic line of force
`(or flux surface) into a magnetic mirror always ex-
`periences a retarding force which is parallel to the
`local direction of the magnetic field and is given by
`the expression 3
`
`F, =
`
`H
`-- dynes,
`
`(4)
`
`where u is the axial distance from the plane of
`symmetry.
`This force, which is the same as that expected on a
`classical magnetic dipole moving in a magnetic field
`gradient, represents the reflecting force of the mirror.
`Integrated up to the peak of the mirrors, (4) yields
`again the binding condition (3).
`Since [k has been assumed constant, (4) may also
`be written in the form
`
`F
`
`- Vu(pH)
`
`(5)
`
`This shows that the quantity p*H acts as a potential
`so that the region between two magnetic mirrors of
`equal strength lies in a potential well between two
`potential maxima of height I/tHmax.
`
`Loss Cones
`It is evident, either from (2), (3) or (5), that it is
`not possible to confine a plasma which is isotropic in
`its velocity conditions-one in which all instantaneous
`spatial directions of motion are allowed-between two
`magnetic mirrors: confinement of an isotropic plasma
`is only possible to contemplate in special cases where
`multiple mirrors might be employed. This limitation
`can be understood in terms of the concept of loss
`cones. The pitch angle, 0, of the helical motion of
`particles moving along a line of force is transformed in
`accordance with a well-known relationship. 4
`sin 0(u) = [R(u)]I sin 0(0)
`
`(6)
`
`where the angle 0(u) is measured with respect to the
`local direction of the magnetic field. R(u) is the
`mirror ratio, evaluated at u, R(u) - H(u)/H(O).
`Expression (6) bears a resemblance to Snell's Law
`of classical optics, which relates refraction angles
`within optically dense media. Here A/R is analogous
`to the index of refraction of Snell's Law. As in the
`optical case, total internal reflection can occur for
`those angles larger than a critical angle, 0, found by
`setting sin 0 equal to its maximum value of 1. Thus
`
`sin 0, = RM- .
`
`(7)
`
`This relation defines the loss cones for particles
`bound between magnetic mirrors, illustrated in Fig. 1.
`All particles with pitch angles lying outside the loss
`cones are bound, while all with pitch angles within the
`loss cone will be lost upon their first encounter with
`either mirror (for equal mirror strengths). It should be
`emphasized that the concept of the mirror loss cone
`
`A
`FIELD CONFIGURATION
`A
`
`377 I
`
`FIELD STRENGTHS
`C
`
`Figure 1. (a) Schematic of magnetic field lines and magnetic
`coils, (b) mirror loss cones, (c) axial magnetic field variation
`
`is in rotation, so that at this point
`motion, W,
`[tH = W. The condition for binding charged particles
`between two magnetic mirrors of equal strength is
`therefore simply that for bound particles
`ttHM > W
`
`(2)
`
`where HM is the strength of the magnetic field at the
`peak of the mirror. This condition may also be ex-
`pressed in terms of field strength and energies through
`use of (1). If H0 is the lowest value of the magnetic
`field between the mirrors, and HM is the peak value at
`the mirror (both being evaluated on the same flux
`surface) then (2) becomes
`
`W/W_±(O) < RM
`
`(3)
`
`where RM = HMIHo
`and
`ratio")
`(the "mirror
`Wi (0) is the value of W at the point where H takes on
`the value H0 .
`It is to be noted that the condition that particles
`be bound does not depend on their mass, charge,
`absolute energy, or spatial position, nor on the
`absolute strength or detailed configuration of the
`magnetic field. Instead, it depends only on the ratios
`of energy components and magnetic field strengths.
`Such an insensitivity to the details of particle types or
`orbits is what is needed to permit the achievement of a
`confined plasma; i.e., a gas composed of charged
`particles of different types, charges and energies.
`The simplicity of the binding conditions reflects the
`insensitivity to detailed motion required to accomplish
`this.
`Further insight into the nature of confinement of a
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`pertains to the velocity space of the trapped particles
`and has nothing to do with the spatial dimensions of
`the confining fields.
`Although the binding of particles between magnetic
`mirrors can be accomplished with fields which are not
`axially symmetric, there are substantial advantages
`to the adoption of axial symmetry. One of these
`advantages arises from the fact that all " magnetic
`bottles " involve magnetic fields with gradients or
`curvature of the magnetic field lines in the confine-
`ment zone,
`the existence of which gives rise to
`systematic drifts of the confined particles across the
`magnetic lines of force. 5 If the particle orbit dia-
`meters are small, compared to the dimensional scale
`of the field gradients or field curvature, these drifts
`will be slow compared to the particle velocities them-
`selves. If directed across the field, however, they
`would still be too rapid to be tolerated and would
`effectively destroy
`the confinement. Furthermore,
`drifts of this type are oppositely directed for electrons
`and ions and may thus give rise to charge separation
`and electric fields within the plasma. These electric
`fields then may induce a general drift of the plasma
`across the field to the walls. However, if the magnetic
`field is axially symmetric, as for example in the mirror
`field configuration of Fig. 1, the particle drifts will
`also be axially symmetric, leading only to a rotational
`drift of the plasma particles around the axis of sym-
`metry, positive ions and electrons drifting in opposite
`directions. However, this will not result in a tendency
`for charge separation to occur, since each flow closes
`on itself.
`Another consequence of the use of axial sym-
`metry is that even though the confined particles may
`be reflected back and forth between the mirrors a very
`large number of times, this fact will not lead to a
`progressive " walking " across the field. In fact, it is
`possible to show that all particles trapped between
`the mirrors are also bound to a high order of approxi-
`mation to the flux surfaces on which they move and
`may not move outward or inward to another flux
`tube (apart from the normal slow diffusion effects
`arising from interparticle collisions).
`Once bound, there is no tendency for particles to
`escape the confining fields, within the assumptions
`made to this point. However, in predicting the con-
`ditions for confinement of a plasma by means of con-
`ditions applying to the individual particles of the
`plasma, one makes the tacit assumption that co-
`operative effects will not act in such a way as to
`destroy the confinement. Such cooperative effects can
`modify the confinement through static or time-varying
`electric fields arising from charge separation, or
`through diamagnetic effects which change the local
`strength of the confining fields themselves. However,
`if the confining magnetic fields are axially symmetric,
`and if the presence of the plasma does not destroy this
`symmetry then, as has already been explained, charge
`separation effects cannot give rise to systematic drifts
`across the field. Similarly, in such a circumstance the
`diamagnetic effect of the plasma can only lead to an
`
`axially symmetric depression of the confining fields in
`the central regions of the confinement zone, but will
`leave the fields at the mirrors essentially unaltered
`(since the density falls nearly to zero at the peak of
`the mirrors, where particles are escaping). Symmetric
`diamagnetic effects therefore tend to increase the
`mirror ratios above the vacuum field value. Of
`course, there will exist a critical value of fl, the ratio
`of plasma pressure to magnetic pressure, above which
`stable confinement is not possible. This critical relative
`pressure will be dependent on various parameters of
`the system, such as: the mirror ratio; the shape,
`symmetry and aspect ratio of the fields; and the
`plasma boundary conditions. Although the precise
`for stability of plasmas confined by
`conditions
`magnetic mirrors are not at this time sufficiently well
`understood theoretically to predict them with con-
`fidence, there is now agreement that it should be
`possible to confine plasmas with a substantial value of
`g3 between magnetic mirrors. 6 This conclusion is borne
`out by the experiments here reported, which indicate
`stable confinement. It should be emphasized, however,
`that, encouraging as this may be, neither the theoreti-
`cal predictions nor the experimental results are yet
`sufficiently advanced to guarantee that plasmas of the
`size, temperature and pressure necessary to produce
`self-sustaining fusion reactions in a Mirror Machine
`would be stable. As in all other known " magnetic
`bottles " the ultimate role of plasma instabilities has
`not yet been determined in the Mirror Machine.
`
`LOSS PROCESSES
`Non-Adiabatic Effects
`Although it has been shown that trapping conditions
`based on adiabatic invariants predict that a plasma
`might,
`in principle, be confined within a Mirror
`Machine for indefinitely long periods of time, it is
`clear that mechanisms will exist for the escape of
`particles, in spite of the trapping.
`One might first of all question the validity of the
`assumption of constant magnetic moment,
`since
`trapping depends critically on this assumption. It
`is clear that this assumption cannot be exactly satis-
`fied in actual magnetic fields, where particle orbits
`are not infinitesimal compared to the dimensions of the
`confining magnetic field.
`It can be seen from first principles, as for example
`shown by Alfvfn 2 that the magnetic moment will be
`very nearly a constant in situations where the mag-
`netic field varies by only a small amount in the course
`of a single rotation period of the particle. It might
`also be suspected, in the light of the analogy between
`this problem and the general theory of non-adiabatic
`effects of classical mechanics, that the deviations from
`adiabaticity should rapidly diminish as the relative
`orbit size is reduced. Kruskal7 has shown that the
`convergence is indeed rapid but his results are not
`readily applicable
`to the Mirror Machine. Using
`numerical methods, however, it has been shown 8 : (a)
`that the fluctuations in magnetic moment associated
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`
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`
`with non-adiabatic effects are of importance only for
`relatively large orbits, (b) that these fluctuations seem
`to be cyclic in nature, rather than cumulative, and
`(c) that they diminish approximately exponentially
`with the reciprocal of the particle orbit size, so that
`it should always be possible to scale an experiment
`in such a way as to make non-adiabatic orbit effects
`negligible. The results may be roughly summarized
`by noting that, for the typical orbits which were
`considered, the maximum amplitude of the fractional
`changes in the magnetic moment, which occurred
`after successive periods of back-and-forth motion
`of trapped particles, could be well represented by an
`expression of the form
`
`= ae-5/
`
`(8)
`
`where v = 27rm/L, i.e., the mean circumference of the
`particle orbit divided by the distance between the
`mirrors. The mirror fields were represented by the
`function H, = Ho [I + a cos uI(p)] plus the appro-
`priate curl-free function for Hr. Here, in dimensionless
`form, u = 2irz/L and p = 27rr/L. With a = 0.25,
`typical values of the constants a and b were in the
`range 4 < a < 6, 1.5 < b < 2, for various radial
`positions of the orbits. From these values it can be
`seen that provided v < 0.2, the variations in /- are
`totally negligible, so that the adiabatic orbit approxi-
`mation is well satisfied. For example, if L = 100 cm
`then all orbits with mean radii less than about 3 cm
`to behave adiabatically. This
`can be considered
`the minimum values of
`imposes restrictions on
`magnetic fields which can be used, or on the minimum
`size of the confinement zones, but it is clear that, as
`the scale of the apparatus is increased, the assumption
`increasingly well
`of orbital adiabaticitv becomes
`satisfied.
`
`Collision Losses
`Even under conditions where the adiabatic invari-
`ants establish effective trapping of particles, there still
`remains a simple and direct mechanism for the loss of
`particles from a mirror machine. This is, of course, the
`mechanism of interpaiticle collisions, the mechanism
`which limits the confinement time of any stable,
`magnetically confined plasma. Collisions can induce
`changes in either the magnetic moment or energy
`of a trapped particle, and thus can cause its velocity
`vector to enter the escape cone. The dominant collision
`cross section in a totally ionized plasma is the Coulomb
`cross section, which varies inversely with the square
`of the relative energy of the colliding particles. Thus
`the rate of losses (if dominated by collisions) can
`be reduced by increasing the kinetic temperature of
`the plasma. The basic rate of these loss processes may
`be estimated by consideration of the "relaxation"
`time of energetic particles in a plasma, as calculated by
`Chandrasekhar or by Spitzer. In this case, the relevant
`quantity is the mean rate of dispersion in pitch angle
`of a particle as a result of collisions, since, if a given
`trapped particle is scattered through a large angle in
`velocity space, the probability is large that it will have
`
`been scattered into the escape cone and thus lost. As is
`usual in a plasma, distant collisions (within a Debye
`sphere) play a greater role than single scattering
`events. The time for the growth of the angular dis-
`persion in this (multiple) scattering process for a
`particle of given energy is governed by the relation
`
`where
`
`2 =
`
`0
`
`t, D
`
`M 2v3
`iD = rue4 9(x) log A'
`
`-ll and v are the mass and velocity of the scattered
`particle, x 2 = W/kT = lMv2 kT and log A has the
`usual value 5 of about 20. X(x) is a slowly varying
`function of x and is approximately equal to 0.5 for
`typical values.
`In terms of deuteron energies in kev,
`
`(11)
`
`ID = 2.6 x 101°I ' n seconds.
`For 02 = 1, the scattering time becomes equal to t.
`Thus tD represents a rough estimate of the confinement
`time of ions in a Mirror Machine. It is clear that the
`confinement time will also depend on the mirror ratio
`R, but detailed calculations show that for large values
`of this ratio, the confinement varies only slowly
`with R.
`Some numerical values are of interest in this con-
`11' = 0.01 kev, and n = 1014, a
`nection. Suppose
`mean particle energy and density which might be
`achieved in a simple discharge plasma. In this case
`tD = 0.26 psec. This means that the confinement of
`low temperature plasmas by simple mirrors will be of
`very short duration, unless means for rapid heating
`are provided, which would extend the confinement
`time. On the other hand, for W = 150 kev, the same
`particle density would give tD = 0.5 sec, which is long
`enough to provide adequate confinement for experi-
`mental studies and is within a factor of about 20 of the
`mean reaction time of a tritium-deuteron plasma at a
`corresponding temperature. Since the energy released
`in a single nuclear reaction would be about 100 times
`the mean energy of the plasma particles, it can be seen
`that the possibility exists for producing an energetically
`self-sustaining reaction, with a modest margin of
`energy profit, in this case about 4 to 1.
`The problem of end losses may be more precisely
`formulated by noting that these losses arise from
`binary collision processes, so that it should be possible
`at all times to write the loss rate in the form
`av>sf(R)
`
`.h =
`
`-2(
`
`(12)
`
`where <V>s represents a scattering rate parameter and
`f(R) measures the effective fractional escape cone of
`the mirrors for diffusing particles. If Kav)s remains
`approximately constant during the decay, then inte-
`gration of the equation shows that a given initial
`density will decay with time as
`n = 0-~~)(13)
`
`where
`
`- =
`
`[o UV/sf(R)] - 1 .
`
`(14)
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`UCRL PYROTRON PROGRAM
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`time approximation consists of
`The relaxation
`setting f(R) = 1-i.e., ignoring the dependence on
`mirror ratio, thereby overestimating the loss rate-
`and, at the same time, approximating the true value
`of noKaV>s by 1/tD, which tends to underestimate the
`loss rate. Thus, in this approximation, the transient
`decay of the plasma in a Mirror Machine is given by
`(15)
`
`0tD/(t + tD).
`
`It =
`
`In this approximation, tD represents the time for
`one-half of the original plasma to escape through the
`mirrors. Now,
`the instantaneous rate of nuclear
`reactions which could occur in the plasma is pro-
`portional to n 2. Integrating n2 from (15) over all time,
`it is found that the total number of reactions which
`will occur is the same as that calculated by assuming
`that the density has the constant value no for time tD
`and then immediately drops to zero; i.e., number of
`reactions is proportional to no2tD.
`Actually, although they correctly portray the basic
`physical processes involved in end losses, estimates of
`confinement time based on simple relaxation con-
`siderations are likely to be in error by factors of two
`or more. To obtain accurate values of the confinement
`time more sophisticated methods are required. Judd,
`McDonald and Rosenbluth, 9 and others, 8 have applied
`the Fokker-Planck equation to this problem and
`have derived results which should be much closer to
`the true situation, even though it was necessary to
`introduce simplifying approximations in their cal-
`culations. They find that calculations based on the
`simple relaxation considerations tend to overestimate
`the confinement times. They are also able to calculate
`explicitly the otherwise intuitive result that the mean
`energy of the escaping group of particles is always
`substantially less than the mean energy of the re-
`maining particles, a circumstance which arises because
`low energy particles are more rapidly scattered than
`high energy ones.
`The most detailed results in these end loss calcula-
`tions have been obtained by numerical integration.
`However, before these results were obtained, D. Judd,
`W. McDonald, and M. Rosenbluth derived an approxi-
`mate analytic solution which, in many cases, differs
`only slightly from the more accurate numerical cal-
`culations. Their results can be expressed by two equa-
`tions which describe the dominant mode of decay of
`an eigenvalue equation for the diffusion of particles
`in the velocity space of the Mirror Machine.
`The first equation, that for the density, is:
`-n 2[ w(ea/m2) v-x>v - 2> log A]A(R),
`i
`
`(16)
`
`where the angle brackets denote averages over the
`particle distribution and log A is the screening factor. 5
`The eigenvalue A(R) is closely approximated by the
`expression A(R) = I/logio(R), showing that the con-
`finement time varies linearly with the mirror ratio, at
`small mirror ratios, but that it varies more slowly at
`large values of R. We see immediately from the form
`of the equation that one can define a scattering time
`as in Eq. (14):
`
`{[ ,i(noeaim2vo3)log A][vo 3<V- 1><v-2,>]A(R)}- 1.
`4
`(17)
`
`The term in the first bracket is almost identical with
`that for the relaxation time of a particle with the
`mean velocity v0 . The velocity averages give rise to
`small departures from the simple relaxation values
`but, as noted, the corrections are usually not large.
`In a similar way, an equation can be written for the
`rate of energy transport through the mirror by par-
`ticle escape. The basic rate for this is, of course,
`simply given by the value of iTs; but W,
`the mean
`energy of escaping particles, as noted, is not the same
`as the mean energy of the remaining particles. They
`find, for the rate of energy loss:
`
`(18)
`-n2[ft(e4/m)<v1> log A]A(R).
`n, s -
`Since the value of <v- '> is not particularly sensitive
`to the velocity distribution, one may calculate this
`for a Maxwellian distribution without committing
`excessive error.
`The mean energy of the escaping ions, W,;, may be
`evaluated from the equations. Dividing (18) by (16),
`Ws is seen to be M<v-2> -1. Approximating the actual
`distribution by a Maxwellian, Ws turns out to be
`or - of the Maxwellian mean energy. This is
`2kT,
`roughly the same value as was obtained by the more
`accurate numerical calculations.
`As far as eventual practical applications are con-
`cerned, the over-all result of the detailed end loss
`calculations is to show that although a power balance
`can in principle be obtained, both with the DT and
`DD reactions, by operation at sufficiently high tem-
`peratures, the margin is less favorable than the rough
`calculations indicated. Thus, any contemplated appli-
`cation of the Mirror Machine to the generation of
`power would doubtless require care in minimizing or
`effectively recovering the energy carried from the
`confinement zone by escaping particles. Some possible
`ways by which this might be accomplished will be
`discussed in sections to follow. Other methods to re-
`duce end losses through magnetic mirrors have been
`suggested and are under study. One of these, involving
`a rotation of the plasma to "enhance"
`the mirror
`effect, is under study at this Laboratory and at the
`Los Alamos Scientific Laboratory.
`In the present Mirror Machine program, scatter-
`ing losses impose a condition on the experimental use
`of simple mirror systems for the heating and confine-
`ment of plasmas. This condition is that operations
`such as injection and heating must be carried out in
`times shorter than the scattering times. These require-
`ments can be readily met, however, in most circum-
`stances so that end losses do not present an appreciable
`barrier to the studies.
`
`Ambipolar Effects
`Since the scattering rate for electrons is more rapid
`than for ions of the same energy, the intrinsic end loss
`rate for electrons and ions will be markedly different.
`In an isolated plasma this situation will not persist,
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`since a difference in escape rates will inevitably result
`in establishing a plasma potential which equalizes the
`rate. In ordinary discharge plasmas, where this effect
`also appears, this " ambipolar " loss rate is always
`dominated by the slower species of the plasma. This
`situation seems to apply also to plasmas confined in the
`Mirror Machine. Although many different cases are
`possible, not all of which are understood, the role of
`ambipolar effects seems mainly to be to introduce a
`(usually) small correction to the end loss rate as cal-
`culated from ion-ion collisions. For example, in the
`is
`important case where the electron temperature
`small compared with the ion temperature, Kaufman 10
`has shown that ambipolar phenomena establish a
`positive plasma potential which, in effect, changes the
`mirror ratio for the ions to a somewhat smaller value
`given by the expression
`Reff = R[l +y(TeiTi)]- 1,
`(19)
`where y is a constant of order unity. For cases of
`practical interest, the resulting correction to the ion
`is small. However, the precise role of
`loss rates
`ambipolar diffusion effects and the electric potentials
`to which they give rise is not well understood, especi-
`ally with regard to plasma stability, and must, there-
`fore, be labeled as part of the unfinished business of
`the Mirror Machine program.
`Confinement of Impurities
`In the study of magnetically confined plasmas, and
`in their eventual practical utilization, contamination
`of the plasma by unwanted impurities presents a
`serious problem. Since the plasma particle densities
`which are of present and future interest are about
`1014-1015 cm - 3, the presence of impurities to the ex-
`tent of even a small fraction of a microgram per liter
`represents a sizeable amount of contamination, per-
`from
`Impurities usually originate
`centage-wise.
`adsorbed layers on the chamber walls, the release of
`even a small fraction of an atomic monolayer corre-
`sponding to a large degree of contamination.
`Impurities of high atomic number greatly increase
`the radiation losses from the plasma. At temperatures
`of a few million degrees the radiation loss mechanism
`is principally from electron-excited optical transitions
`of incompletely stripped impurity ions. In this case,
`the intrinsic radiation rates per impurity ion can be as
`high as one million times the radiation rate of a hydro-
`gen ion. At thermonuclear temperatures, the stripping
`becomes more nearly complete, so that the radiation
`less intense, finally
`rate from impurities becomes
`approaching the bremsstrahlung value, Z 2 times the
`loss rate for hydrogen. But even in this case, because
`of the relatively narrow margin between the thermo-
`nuclear power production and the radiation loss rates
`from even a perfectly pure hydrogenic plasma, the
`concentration of high-Z impurities must be kept to a
`minimum. The actual level of impurities in any
`magnetically confined plasma will be determined by a
`competition between their rate of influx and the
`degree to which they are confined by the magnetic
`fields.
`
`In the light of these facts, it is important to note
`that in the Mirror Machine, the confinement of im-
`purity ions should be much poorer than for energetic
`hydrogen ions. Thus there tends to exist a natural
`"purification" mechanism discriminating
`against
`the presence of impurities in the plasma.
`This happy circumstance arises from three general
`causes. First, the scattering rate for stripped high-Z
`ions is more rapid than for hydrogen ions of the
`same energy. Second, impurity ions originating from
`the walls will always have much lower energies than
`ions. This will
`the mean energy of the confined
`increase their loss rate by scattering. Third, in the
`"normal" high temperature confinement condition
`in the Mirror Machine, where ion energies are much
`greater than the electron temperature, the sign of the
`plasma potential should be positive, so that low energy
`positive ions cannot be bound at all, but will be
`actively expelled. These circumstances could be of an
`importance equal to that of adequate confinement in
`the eventual problems of establishing a power balance
`from fusion reactions.
`
`BASIC OPERATIONS
`
`In order to create, heat and confine a hot plasma in
`any magnetic bottle a series of operations is always
`required. In the Mirror Machine a somewhat different
`philosophy of these operations has been adopted from
`that used in most other approaches, for example,
`those utilizing the pinch effect. In those approaches,
`one starts with a chamber filled with neutral gas and
`then attempts to ionize the gas, heat and confine the
`resulting plasma. By contrast, in the Mirror Machine a
`highly evacuated chamber is employed, into the center
`of which a relatively energetic plasma is injected,
`trapped and subsequently further heated. Since the
`Mirror Machine possesses "open" ends through which
`the plasma can be introduced by means of external
`sources, injection methods can be employed which are
`not possible in systems of toroidal topology.
`By using the magnetic mirror effect in various ways,
`it is possible to perform several basic operations on a
`plasma. These are employed in the Mirror Machine to
`create, heat, control and study the plasma. In addition
`to simple confinement the following operations are
`used.
`1. Radial compression-adiabatic compression of
`the plasma performed by uniformly increasing the
`strength of the confining fields.
`2. Axial compression-adiabatic compression per-
`formed by causing the mirrors to move closer together.
`the
`3. Transfer or axial acceleration-pushing
`region
`to
`plasma axially from one confinement
`another by moving the mirrors.
`the direction of
`4. "Valve" action-controlling
`diffusion of the plasma by weakening or strengthening
`one mirror relative to the other.
`In the experimental study of these operations most
`of the emphasis has been placed on achieving condi-
`tions where the assumption of adiabaticity is valid and
`
`IPR2014-00828
`GlobalFoundries 1222
`
`

`

`UCRL PYROTRON PROGRAM
`
`gas, since there are two degrees of freedom associated
`with rotational energy. For this case, the gas constant,
`y, has the value 2 and the heating varies linearly with
`- n. In the case