Radiant energy – Ionic separation or analysis – Cyclically varying ion selecting field means
Reexamination Certificate
2000-06-23
2003-02-04
Berman, Jack (Department: 2881)
Radiant energy
Ionic separation or analysis
Cyclically varying ion selecting field means
C250S282000, C250S283000, C209S012100, C209S226000, C210S222000, C210S695000, C210S748080, C204S156000, C095S028000, C096S002000, C096S003000
Reexamination Certificate
active
06515281
ABSTRACT:
FIELD OF THE INVENTION
The present invention pertains generally to devices that are useful for separating particles (ions) of a predetermined mass from other charged particles in a multi-species plasma. More particularly, the present invention pertains to devices that accelerate selected particles (ions) at their cyclotron frequencies by using a resonant electric field to segregate and separate the selected ions from the plasma. The present invention is particularly, but not exclusively, useful for employing a stochastically generated electric field, having a predetermined band of frequencies, that will resonate with selected particles having respective cyclotron frequencies within the band of frequencies to thereby separate the selected particles from other charged particles in a plasma.
BACKGROUND OF THE INVENTION
Cyclotron resonance occurs under conditions wherein electromagnetic power is coupled into a system of charged particles. The consequence of this coupling is a phenomenon known as ion cyclotron resonance heating (ICRH). Simply stated, ICRH occurs when a charged particle (e.g. an ion) is positioned in a uniform magnetic field, and the frequency of the electromagnetic power is resonant with the cyclotron frequency of the charged particle. The result is that the charged particle is accelerated into a spiral path by the absorption of energy from the electromagnetic power.
In a basic cyclotron, the charged particles are accelerated by electromagnetic waves having a fixed frequency. It happens, however, that the maximum ion energy that can be attained using a fixed frequency is limited because there is a relativistic mass increase for the ions at very high energies. This increase in mass then breaks the synchronous relationship for resonance between the frequency of the electromagnetic power and the cyclotron frequency of the charged particles. To overcome this difficulty, the synchrocyclotron was invented to modulate the electromagnetic power, and to thereby compensate for the relativistic mass increase. The dynamic modulation of electromagnetic power that is required to maintain an operation that is synchronous with relativistic mass increases can, however, be problematical. Consequently, the stochastic cyclotron was invented to effectively make such an operation steady state. In essence, a stochastic cyclotron is able to provide random inputs, within a specified frequency range, which will statistically accelerate ions in the stochastic cyclotron so long as the relativistic mass increases and the consequent cyclotron frequencies of the ions remain within the range.
Insofar as plasma mass filters are concerned, it is known that the basic principles of ICRH can be applied to a multi-species plasma to separate charged particles of a selected mass from other particles in the plasma. For example, such a procedure is disclosed in U.S. Pat. No. 5,442,481, which issued to Louvet on May 13, 1994 for an invention entitled “DEVICE FOR ISOTOPE SEPARATION BY ION CYCLOTRON RESONANCE.” Also an exemplary plasma mass filter has been recently disclosed by Ohkawa in U.S. Pat. No. 6,096,220 issued on Aug. 1, 2000 for an invention entitled “PLASMA MASS FILTER.” This invention separates particles based on the magnitude of their mass charge ratio. Using this technology, it may sometimes be desirable to isolate and separate a group of charged particles that have nearly the same mass numbers. For instance, in one application it would be desirable to remove transuranic elements or fission fragments from nuclear waste. In this case the transuranic elements have mass numbers in the range of 235 to 240 and the fission fragments will have mass numbers in the range of 80 to 120. Most of the non-radioactive material will have mass numbers less than 60. In such a situation, it may be desirable to remove all of the particles having mass numbers in the range of 235 to 240 as well as particles having mass numbers in the range of 80 to 120. The mathematical development which describes how this condition can be realized is helpful.
In describing the acceleration of the ions, consider an example where the electric field E
x
is uniform and in x-direction. (The static magnetic field is in z-direction.) The time dependence is given by
E
x
=
∫
ω
1
ω
2
F
[
ω
]
cos
ω
t
ⅆ
ω
(
Eq
.
1
)
where F is the Fourier component. We choose the white noise spectrum between the frequencies &ohgr;
1
and &ohgr;
2
, i.e.
F[&ohgr;]=F &ohgr;
2
≧&ohgr;≧&ohgr;
1
F[&ohgr;]=0 &ohgr;>&ohgr;
2
and &ohgr;<&ohgr;
1
(Eq. 2)
The equations of the motion of the ions are given by
Mdv
x
/dt=ev
y
B+eE
x
Mdv
y
/dt=−ev
x
Mdv
z
/dt=0 (Eq. 3)
where M is the mass of the ions and B is the static magnetic field. We define u by
u=exp [i&OHgr;t][v
x
+iv
y
]
where &OHgr;=eB/M, and obtain
u
=
[
e
/
2
i
M
]
∫
ω
1
ω
2
F
[
ω
]
[
{
exp
[
i
Ω
t
+
i
ω
]
-
1
}
[
Ω
+
ω
]
-
1
+
{
exp
[
i
Ω
t
-
i
ω
t
]
-
1
}
[
Ω
-
ω
]
-
1
]
ⅆ
ω
+
u
0
(
Eq
.
4
)
where the subscript 0 denotes the value at t=0.
The first term does not contain the resonance term and is neglected. The resonant part with F[l] given by Eq. 2 becomes
u
=
[
e
F
/
2
i
M
]
∫
ω
1
ω
2
{
exp
[
i
Ω
t
-
i
ω
t
]
-
1
}
[
Ω
-
ω
]
-
1
ⅆ
ω
+
u
0
(
Eq
.
5
)
The above expression can be written in terms of Sine integral Si and Cosine integral Ci,
u=[eF/2M]{{Si[&ohgr;
2
t−&OHgr;t]+Si[&OHgr;t−&ohgr;
1
t]+
i{Ci[&ohgr;
2
t−&OHgr;t]+Ci[&OHgr;t−&ohgr;
1
t]−
1n[&ggr;{&ohgr;
2
−&OHgr;}t]−1n[&ggr;{&OHgr;−&ohgr;
1
}t]}}+
u
0
(Eq. 6)
where &ggr;=1.781.
For small values of the argument, consider
Si[&xgr;]→&xgr;
and
Ci[&xgr;]→
1
n[&ggr;&xgr;]
and obtain
u≈[eF/
2
M][&ohgr;
2
−&ohgr;
1
]t
(Eq. 7)
where u
0
=0 is assumed.
The electric field strength E is given by
E=[&ohgr;
2
&ohgr;
1
]F
and Eq. 7 becomes
u≈[eE/
2
M]t
(Eq. 8)
In the asymptotic limit,
Si[&xgr;]→&pgr;/
2−cos &xgr;/&xgr;
Ci[&xgr;]→
sin &xgr;/&xgr;
By neglecting the logarithmic terms we obtain
u →[eF/
2
M]&pgr;=[eE/
2
M]&pgr;[&ohgr;
2
−&ohgr;
1
]
−1
(Eq. 9)
The velocities given by Eq. 8 and Eq. 9 show that the ions are accelerated initially at the rate equal to that for the single frequency resonance and the acceleration saturates after &OHgr;/{2[&ohgr;
2
−&ohgr;
1
]} cyclotron cycles.
When the frequency interval &ohgr;
1
to &ohgr;
2
does not contain the cyclotron frequency &OHgr;, i.e.
&OHgr;<&ohgr;
1
<&ohgr;
2
or &OHgr;>&ohgr;
2
>&ohgr;
1
the real part of the velocity given by Eq. 1 becomes
Reu=[eF/
2
M]{Si[&ohgr;
2
t−&OHgr;t]−Si[&ohgr;
1
t−&OHgr;t]} &OHgr;<&ohgr;
1
<&ohgr;
2
(Eq. 10)
or
=[eF/
2
M]{Si[&OHgr;t−&ohgr;
1
t]−Si[&OHgr;t−&ohgr;
2
t]} &OHgr;>&ohgr;
2
&ohgr;
1
In either case,
Reu→
0 for
t→∞
The above expression shows that the acceleration
Archimedes Technology Group, Inc.
Berman Jack
Nydegger & Associates
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