Tandem plasma mass filter

A tandem plasma mass filter for separating low-mass particles from high-mass particles in a multi-species plasma includes a cylindrical shaped wall which surrounds a hollow chamber. A magnet is mounted on the wall to generate a magnetic field that is aligned substantially parallel to the longitudinal axis of the chamber. Also, an electric field is generated which is substantially perpendicular to the magnetic field and which, together with the magnetic field, creates crossed magnetic and electric fields in the chamber. Importantly, the electric field has a positive potential on the axis relative to the wall which is usually zero potential. When a vapor is injected into the chamber and ionized, the resultant multi-species plasma interacts with the crossed magnetic and electric fields to eject high-mass particles into the wall surrounding the chamber. On the other hand, low-mass particles are confined in the chamber during their transit therethrough to separate the low-mass particles from the high-mass particles. The demarcation between high-mass particles and low-mass particles is a cut-off mass M.sub.c which is established by setting the magnitude of the magnetic field strength, B.sub.z, the positive voltage along the longitudinal axis, V.sub.ctr, and the radius of the cylindrical chamber, "a". pe1 53M.sub.c can then be determined with the expression: M.sub.c =ea.sup.2 (B.sub.z).sup.2 /8V.sub.ctr.

FIELD OF THE INVENTION
 The present invention pertains generally to devices and apparatus which are
 capable of separating charged particles in a plasma according to their
 respective masses. More particularly, the present invention pertains to
 energy efficient filtering devices which extract particles of a particular
 mass range from a multi-species plasma. The present invention is
 particularly, but not exclusively, useful as an energy efficient, high
 throughput filter for separating low-mass particles from high-mass
 particles.
 BACKGROUND OF THE INVENTION
 The general principles of operation for a plasma centrifuge are well known
 and well understood. In short, a plasma centrifuge generates forces on
 charged particles which will cause the particles to separate from each
 other according to their mass. More specifically, a plasma centrifuge
 relies on the effect crossed electric and magnetic fields have on charged
 particles. As is known, crossed electric and magnetic fields will cause
 charged particles in a plasma to move through the centrifuge on respective
 helical paths around a centrally oriented longitudinal axis. As the
 charged particles transit the centrifuge under the influence of these
 crossed electric and magnetic fields they are, of course, subject to
 various forces. Specifically, in the radial direction, i.e. a direction
 perpendicular to the axis of particle rotation in the centrifuge, these
 forces are: 1) a centrifugal force, F.sub.c, which is caused by the motion
 of the particle; 2) an electric force, F.sub.E, which is exerted on the
 particle by the electric field, E.sub.r ; and 3) a magnetic force,
 F.sub.B, which is exerted on the particle by the magnetic field, B.sub.z.
 Mathematically, each of these forces are respectively expressed as:
EQU F.sub.c =Mr.omega..sup.2 ;
EQU F.sub.E =eE.sub.r ;
 and
EQU F.sub.B =er.omega.B.sub.z.
 Where:
 M is the mass of the particle;
 r is the distance of the particle from its axis of rotation;
 .omega. is the angular frequency of the particle;
 e is the electric charge of the particle;
 E is the electric field strength; and
 B.sub.z is the magnetic flux density of the field.
 In a plasma centrifuge, it is universally accepted that the electric field
 will be directed radially inward. Stated differently, there is an increase
 in positive voltage with increased distance from the axis of rotation in
 the centrifuge. Under these conditions, the electric force F.sub.E will
 oppose the centrifugal force F.sub.c acting on the particle, and depending
 on the direction of rotation, the magnetic force either opposes or aids
 the outward centrifugal force. Accordingly, an equilibrium condition in a
 radial direction of the centrifuge can be expressed as:
EQU .SIGMA.F.sub.r =0 (positive direction radially outward)
EQU F.sub.c -F.sub.E -F.sub.B =0
EQU Mr.omega..sup.2 -eE.sub.r -er.omega.B.sub.z =0 (Eq. 1)
 It is noted that Eq. 1 has two real solutions, one positive and one
 negative, namely:
 ##EQU1##
 For a plasma centrifuge, the intent is to seek an equilibrium to create
 conditions in the centrifuge which allow the centrifugal forces, F.sub.c,
 to separate the particles from each other according to their mass. This
 happens because the centrifugal forces differ from particle to particle,
 according to the mass (M) of the particular particle. Thus, particles of
 heavier mass experience greater F.sub.c and move more toward the outside
 edge of the centrifuge than do the lighter mass particles which experience
 smaller centrifugal forces. The result is a distribution of lighter to
 heavier particles in a direction outward from the mutual axis of rotation.
 As is well known, however, a plasma centrifuge will not completely
 separate all of the particles in the aforementioned manner.
 As indicated above in connection with Eq. 1, a force balance can be
 achieved for all conditions when the electric field E is chosen to confine
 ions, and ions exhibit confined orbits. In the plasma filter of the
 present invention, unlike a centrifuge, the electric field is chosen with
 the opposite sign to extract ions. The result is that ions of mass greater
 than a cut-off value, M.sub.c, are on unconfined orbits. The cut-off mass,
 M.sub.c, can be selected by adjusting the strength of the electric and
 magnetic fields. The basic features of the plasma filter can be described
 using the Hamiltonian formalism.
 The total energy (potential plus kinetic) is a constant of the motion and
 is expressed by the Hamiltonian operator:
EQU H=e.PHI.+(P.sub.R.sup.2 +P.sub.z.sup.2)/(2M)+(P.sub..theta. -e.PSI.).sup.2
 /(2Mr.sup.2)
 where P.sub.R =MV.sub.R, P.sub..theta. =MrV.sub..theta. +e.PSI., and
 P.sub.z =MV.sub.z are the respective components of the momentum and e.PHI.
 is the potential energy. .PSI.=r.sup.2 B.sub.z /2 is related to the
 magnetic flux function and .PHI.=.alpha..PSI.+V.sub.ctr is the electric
 potential. E=-.gradient..PHI. is the electric field which is chosen to be
 greater than zero for the filter case of interest. We can rewrite the
 Hamiltonian:
EQU H=e.alpha.r.sup.2 B.sub.z /2+eV.sub.ctr +(P.sub.R.sup.2
 +P.sub.z.sup.2)/(2M)+(P.sub..theta. -er.sup.2 B.sub.z /2).sup.2
 /(2Mr.sup.2)
 We assume that the parameters are not changing along the z axis, so both
 P.sub.z and P.sub..theta. are constants of the motion. Expanding and
 regrouping to put all of the constant terms on the left hand side gives:
EQU H-eV.sub.ctr -P.sub.z.sup.2 /(2M)+P.sub..theta..OMEGA./2=P.sub.R.sup.2
 /(2M)+(P.sub..theta..sup.2 /(2Mr.sup.2)+(M.OMEGA.r.sup.2
 /2)(.OMEGA./4+.alpha.)
 where .OMEGA.=eB/M.
 The last term is proportional to r.sup.2, so if .OMEGA./4+.alpha.&lt;0 then,
 since the second term decreases as 1/r.sup.2, P.sub.R.sup.2 must increase
 to keep the left-hand side constant as the particle moves out in radius.
 This leads to unconfined orbits for masses greater than the cut-off mass
 given by:
EQU M.sub.c =e(B.sub.2 a).sup.2 /(8V.sub.ctr) where we used:
EQU .alpha.=(.PHI.-V.sub.ctr)/.PSI.=-2V.sub.ctr /(a.sup.2 B.sub.z) (Eq. 2)
 and where a is the radius of the chamber.
 So, for example, normalizing to the proton mass, M.sub.p, we can rewrite
 Eq. 2 to give the voltage required to put higher masses on loss orbits:
EQU V.sub.ctr &gt;1.2.times.10.sup.-1 (a(m)B(gauss)).sup.2 /(M.sub.c /M.sub.p)
 Hence, a device radius of 1 m, a cutoff mass ratio of 100, and a magnetic
 field of 200 gauss require a voltage of 48 volts.
 The same result for the cut-off mass can be obtained by looking at the
 simple force balance equation given by:
EQU .SIGMA.F.sub.r =0 (positive direction radially outward)
EQU F.sub.c +F.sub.E +F.sub.B =0
EQU Mr.omega..sup.2 +eEr-er.omega.B.sub.z =0 (Eq. 3)
 which differs from Eq. 1 only by the sign of the electric field and has the
 solutions:
 ##EQU2##
 so if 4E/rB.sub.z.OMEGA.&gt;1 then .omega. has imaginary roots and the force
 balance cannot be achieved. For a filter device with a cylinder radius
 "a", a central voltage, V.sub.ctr, and zero voltage on the wall, the same
 expression for the cut-off mass is found to be:
EQU M.sub.c =ea.sup.2 B.sub.z.sup.2 /8V.sub.ctr (Eq. 4)
 When the mass M of a charged particle is greater than the threshold value
 (M&gt;M.sub.c), the particle will continue to move radially outwardly until
 it strikes the wall, whereas the lighter mass particles will be contained
 and can be collected at the exit of the device. The higher mass particles
 can also be recovered from the walls using various approaches.
 It is important to note that for a given device the value for M.sub.c in
 equation 3 is determined by the magnitude of the magnetic field, B.sub.z,
 and the voltage at the center of the chamber (i.e. along the longitudinal
 axis), V.sub.ctr. These two variables are design considerations and can be
 controlled. It is also important that the filtering conditions (Eqs. 2 and
 3) are not dependent on boundary conditions. Specifically, the velocity
 and location where each particle of a multi-species plasma enters the
 chamber does not affect the ability of the crossed electric and magnetic
 fields to eject high-mass particles (M&gt;M.sub.c) while confining low-mass
 particles (M&lt;M.sub.c) to orbits which remain within the distance "a" from
 the axis of rotation.
 In all processes which create and then manipulate a plasma, a large amount
 of energy is required. Specifically, energy is required to vaporize and
 ionize the plasma material. On top of this, additional energy is required
 to create the magnetic and electrical fields that are needed to contain
 and manipulate the plasma. Consequently, the economic feasibility of using
 a plasma process such as a plasma mass filter or plasma centrifuge to
 separate one material from another depends significantly on energy
 considerations. Further, the throughput rate and separation efficiency
 also effect the energy input that is required to operate a plasma process.
 In plasma processes such as a plasma mass filter, particles tend to travel
 along magnetic field lines in either direction. Consequently, for
 particles introduced into a magnetic field, approximately half of the
 particles travel in one direction along the magnetic field lines while the
 rest of the particles travel in the opposite direction, along the magnetic
 field lines. For a cylindrical vessel having magnetic field lines that are
 parallel to the cylinder's axis, wherein particles are introduced at one
 end of the vessel, only approximately half of the particles will travel
 toward the second end. The other half of the particles will collect in the
 vessel at the point of introduction. Consequently, for a plasma mass
 filter having a simple cylinder configuration, only about half of the
 material introduced at one end will effectively travel towards the exit at
 the opposite end and thereby undergo separation. A consequence of this is
 that about half of the material will need to be reprocessed.
 In light of the above, it is an object of the present invention to provide
 a plasma mass filter for separation of low-mass particles from high-mass
 particles that is configured to increase energy efficiency, throughput
 rate and separation efficiency. It is another object of the present
 invention to provide a plasma mass filter having twice the throughput as a
 simple cylindrical plasma mass filter by introducing vapors into a
 magnetic field, perpendicular to the magnetic field lines, and to then
 allow half of the plasma that is generated in the filter to travel along
 the magnetic field lines in a first direction toward a first collector and
 the remaining plasma to travel in the opposite direction toward a second
 collector. It is another object of the present invention to provide a
 plasma mass filter for separating low-mass particles from high-mass
 particles that prevents a substantial amount of the particles from exiting
 the vessel at the point of introduction. Yet another object of the present
 invention is to provide a plasma mass filter which is easy to use,
 relatively simple to manufacture, and comparatively cost effective.
 SUMMARY OF THE PREFERRED EMBODIMENTS
 A plasma mass filter for separating low-mass particles from high-mass
 particles in a multi-species plasma includes a cylindrical shaped wall
 which surrounds a hollow chamber and defines a longitudinal axis. Around
 the outside of the chamber is a magnetic coil which generates a magnetic
 field, B.sub.z. This magnetic field is established in the chamber and is
 aligned substantially parallel to the longitudinal axis. Also, at one end
 of the chamber there is a series of voltage control rings which generate
 an electric field, E.sub.r, that is directed radially outward and is
 oriented substantially perpendicular to the magnetic field. With these
 respective orientations, B.sub.z and E.sub.r create crossed magnetic and
 electric fields. Importantly, the electric field has a positive potential
 on the longitudinal axis, V.sub.ctr, and a substantially zero potential at
 the wall of the chamber.
 In operation, the magnitude of the magnetic field, B.sub.z, and the
 magnitude of the positive potential, V.sub.ctr, along the longitudinal
 axis of the chamber are set. A rotating multi-species plasma can then be
 injected into one end of the chamber to interact with the crossed magnetic
 and electric fields. Alternatively, a material in the vapor state can be
 injected into the chamber through an inlet that is positioned
 substantially midway between the cylinder ends. Once injected into the
 chamber, the vapor can then be ionized to create a multi-species plasma by
 exposing the vapor to radiofrequency (rf) energy. A radiofrequency antenna
 can be mounted to the cylindrical wall inside the chamber to create the
 radiofrequency energy required to ionize the vapor. Once ionized, the
 pressure gradient that develops within the plasma will cause the ionized
 particles to travel along the magnetic field lines towards the cylinder
 ends. As described in detail below, low-mass particles will exit the
 cylinder at each cylinder end and high-mass particles will strike and be
 captured by the cylinder wall. More specifically, for a chamber having a
 distance "a" between the longitudinal axis and the chamber wall, B.sub.z
 and V.sub.ctr are set and M.sub.c is determined by the expression:
EQU M.sub.c =ea.sup.2 (B.sub.z).sup.2 /8V.sub.ctr
 Consequently, of all the particles in the multi-species plasma, low-mass
 particles which have a mass less than the cut-off mass M.sub.c (M&lt;M.sub.c)
 will be confined in the chamber during their transit through the chamber.
 On the other hand, high-mass particles which have a mass that is greater
 than the cut-off mass (M&gt;M.sub.c) will be ejected into the wall of the
 chamber and, therefore, will not transit the chamber.

DESCRIPTION OF THE PREFERRED EMBODIMENT
 Referring to FIG. 1, a plasma mass filter is shown and generally designated
 10. As shown, the filter 10 includes a substantially cylindrical shaped
 wall 12 which surrounds a chamber 14, and defines a longitudinal axis 16.
 The actual dimensions of the chamber 14 are somewhat, but not entirely, a
 matter of design choice. Importantly, the radial distance "a" between the
 longitudinal axis 16 and the wall 12 is a parameter which will affect the
 operation of the filter 10, and as clearly indicated elsewhere herein,
 must be taken into account.
 It is also shown in FIG. 1 that the filter 10 includes a plurality of
 magnetic coils 18 which are mounted on the outer surface of the wall 12 to
 surround the chamber 14. In a manner well known in the pertinent art, the
 coils 18 can be activated to create a magnetic field in the chamber 14
 which has a component B.sub.z that is directed substantially along the
 longitudinal axis 16. Additionally, the filter 10 includes a plurality of
 voltage control rings 20, of which the voltage rings 20a-c are
 representative. As shown these voltage control rings 20a-c are located at
 one end of the cylindrical shaped wall 12 and lie generally in a plane
 that is substantially perpendicular to the longitudinal axis 16. With this
 combination, a radially oriented electric field, E.sub.r, can be
 generated. An alternate arrangement for the voltage control is the spiral
 electrode 20d shown in FIG. 2.
 For the plasma mass filter 10, the magnetic field B.sub.z and the electric
 field E.sub.r are specifically oriented to create crossed electric and
 magnetic fields. As is well known to the skilled artisan, crossed electric
 and magnetic fields cause charged particles (i.e. ions) to move on helical
 paths, such as the path 22 shown in FIG. 1. Indeed, it is well known that
 crossed electric and magnetic fields are widely used for plasma
 centrifuges. Quite unlike a plasma centrifuge, however, the plasma mass
 filter 10 for the present invention requires that the voltage along the
 longitudinal axis 16, V.sub.ctr, be a positive voltage, compared to the
 voltage at the wall 12 which will normally be a zero voltage.
 In the operation of the plasma mass filter 10, a rotating multi-species
 plasma 24 can be injected into one end 25 of the chamber 14, as shown in
 FIG. 1. Under the influence of the crossed electric and magnetic fields,
 charged particles confined in the plasma 24 will travel generally along
 helical paths around the longitudinal axis 16 similar to the path 22. More
 specifically, as shown in FIG. 1, the multi-species plasma 24 includes
 charged particles which differ from each other by mass. For purposes of
 disclosure, the plasma 24 includes at least two different kinds of charged
 particles, namely high-mass particles 26 and low-mass particles 28. It
 will happen, however, that only the low-mass particles 28 are actually
 able to transit through the chamber 14.
 In accordance with mathematical calculations set forth above, the
 demarcation between low-mass particles 28 and high-mass particles 26 is a
 cut-off mass, M.sub.c, which can be established by the expression:
EQU M.sub.c =ea.sup.2 (B.sub.z).sup.2 /8V.sub.ctr.
 In the above expression, e is the charge on an electron, a is the radius of
 the chamber 14, B.sub.z is the magnitude of the magnetic field, and
 V.sub.ctr is the positive voltage which is established along the
 longitudinal axis 16. Of these variables in the expression, e is a known
 constant. On the other hand, "a", B.sub.z and V.sub.ctr can all be
 specifically designed or established for the operation of plasma mass
 filter 10.
 Due to the configuration of the crossed electric and magnetic fields and,
 importantly, the positive voltage V.sub.ctr along the longitudinal axis
 16, the plasma mass filter 10 causes charged particles in the
 multi-species plasma 24 to behave differently as they transit the chamber
 14. Specifically, charged high-mass particles 26 (i.e. M&gt;M.sub.c) are not
 able to transit the chamber 14 and, instead, they are ejected into the
 wall 12. On the other hand, charged low-mass particles 28 (i.e. M&lt;M.sub.c)
 are confined in the chamber 14 during their transit through the chamber
 14. Thus, the low-mass particles 28 exit the chamber 14 and are, thereby,
 effectively separated from the high-mass particles 26.
 FIG. 3 shows an embodiment of a plasma mass filter 10 in which the chamber
 14 is formed with a chamber inlet 30 that is positioned substantially
 midway between the ends 32, 34 of the cylinder wall 12. An injector 33 can
 be used to inject a material in the vapor state (vapor 35) through the
 chamber inlet 30 in the direction of arrow 36 and into the chamber 14. For
 purposes of the present invention, any injector 33 known in the pertinent
 art can be used. Once injected into the chamber 14, the vapor 35 can be
 ionized to create a multi-species plasma 24 by exposing the vapor 35 to
 radiofrequency (rf) energy. As shown in FIG. 3, a radiofrequency antenna
 38 can be mounted to the wall 12 inside the chamber 14 to create the
 radiofrequency energy that is required to ionize the vapor 35 into a
 multi-species plasma 24. As shown, the multi-species plasma 24 includes
 high-mass particles 26, low-mass particles 28 and electrons 40.
 Once inside the chamber 14, a pressure gradient that develops within the
 multi-species plasma 24 will cause a portion of the multi-species plasma
 24 to drift towards the end 32 while the remaining multi-species plasma 24
 will drift in the opposite direction towards the end 34. As described
 above, the crossed electric and magnetic fields will cause the
 multi-species plasma 24 to travel in a generally helical path 22 about the
 longitudinal axis 16, as the plasma 24 drifts towards the ends 32, 34. In
 accordance with the mathematics set forth above, however, it will happen
 that only the low-mass particles 28 are actually able to transit through
 the chamber 14 and exit the chamber 14 through the two ends 32, 34. As
 discussed above, the high-mass particles 26 will travel on unconfined
 orbits. These unconfined orbits will cause the high-mass particles 26 to
 strike and be captured by the wall 12.
 While the particular Tandem Plasma Mass Filter as herein shown and
 disclosed in detail is fully capable of obtaining the objects and
 providing the advantages herein before stated, it is to be understood that
 it is merely illustrative of the presently preferred embodiments of the
 invention and that no limitations are intended to the details of
 construction or design herein shown other than as described in the
 appended claims.