USH2171HExpiredUtilityPatentIndex 59
Method and apparatus for modeling cosmic ray effects on microelectronics
Est. expiryDec 31, 2017(expired)· nominal 20-yr term from priority
Inventors:ADAMS JR JAMES HBOBERG PAUL RBROWNSTEIN BRUCE ADIETRICH WILLIAM FFLUECKIGER ERWIN OPETERSEN EDWARD LSHEA MARGARET ASMART DON FSMITH EDWARD CTYLKA ALLAN J
G06F 30/20G06F 2111/10G06F 30/25
59
PatentIndex Score
8
Cited by
10
References
13
Claims
Abstract
An aspect of the present invention is a method and apparatus for computing a geomagnetic transmission function. This apparatus includes a programmed digital computer running modeling software for modeling the transmission of cosmic ray particles through the magnetosphere. The software includes a model representing a solution to the Lorentz equation in a magnetic field given by B=B IGRF (r,t′)+B TSYG (Kp,r,t′). Another aspect of the present invention is a method and apparatus for computing a flux of particles at the outer surface of a satellite comprising, inter alia, an improved method and apparatus for computing a flux of solar heavy ions. This apparatus includes a programmed digital computer running modeling software for modeling the flux of cosmic ray particles through the outer surface of a satellite. Another aspect of the invention is a method and apparatus comprising a programmed digital computer running modeling software for modeling the effect of cosmic rays on microelectronics, where this software embodies at least one of the two foregoing aspects of the invention.
Claims
exact text as granted — not AI-modified1. A method for determining a geomagnetic transmission function for the transmission of a population of particles, said particles having one or more rigidities, to a satellite in a known earth orbit, under known geomagnetic conditions, comprising the steps:
(A) dividing said orbit into a plurality of sequential steps comprising at least a first step and a last step, each sequential pair of said steps being connected at a point, each of said points corresponding to a position of said satellite along said orbit, and specifying a value for Kp and a value for Dst to specify said geomagnetic conditions;
(B) for a plurality of said points, selecting a plurality of arrival directions for the arrival of said particles at said satellites, wherein each of said arrival directions represents either an allowed or a forbidden trajectory of one of said particles; and
(C) for each of said arrival directions at each of said plurality of said points, determining whether said arrival direction represents an allowed or a forbidden trajectory by tracing a path of said particle to arrive at said point with said arrival direction, until said particle path intersects a boundary of earth's magnetosphere, thereby indicating an allowed trajectory, or until said particle path intersects either earth's atmosphere or earth's surface, thereby indicating a forbidden trajectory, wherein said tracing of said path is performed by integrating in the time domain the Lorentz equation
F=mγdv/d(−t′)=−Qv×B
wherein F is the force vector acting on said particle, m is mass γ is 1/(1−v 2 /c 2 ) −1/2 , v is said particle's velocity vector, t′ is the travel time of said particle, Q is the charge of said particle, and B is the magnetic field vector acting on said particle, wherein B is given by
B=B IGRF (r,t′)+B TSYG (Kp,r,t′)
where B IGRF is the International Geomagnetic Reference Field promulgated by the International Association of Geomagnetism and Aeronomy, and B TSYG is the modified Tsyganenko field given by the sum of B Xmg (T) +B Ymg (T) +B Zmg (T) +B Xmg (RC) +B Ymg (RC) +B Zmg (RC) +B Xsm (C) +B Ysm (C) +B Zsm (C) +B Xsm (M) +B Ysm (M) +B Zsm (M) , wherein coordinates in the solar magnetospheric system are denoted sm, and wherein coordinates in the solar magnetic coordinate system are denoted mg; and wherein
B X (T) =Q t x z r ;
B Y (T) =Q t y z r ;
B
Z
(
T
)
=
W
(
x
,
y
)
S
T
(
C
1
+
C
2
a
T
+
ξ
T
S
T
2
)
+
x
∂
W
∂
x
+
y
∂
W
∂
y
S
T
+
a
T
+
ξ
T
×
(
C
1
+
C
2
S
T
)
+
B
x
(
T
)
∂
z
s
∂
x
+
B
Y
(
T
)
∂
z
s
∂
y
-
Q
T
D
T
(
x
∂
D
T
∂
x
+
y
∂
D
T
∂
y
)
wherein
W
(
x
,
y
)
=
0.5
(
1
-
x
-
x
0
[
(
x
-
x
0
)
2
+
D
x
2
]
1
2
)
×
(
1
+
y
2
D
y
2
)
-
1
wherein
Q
T
=
W
(
x
,
y
)
ξ
T
S
T
[
C
1
S
T
+
a
T
+
x
T
+
C
2
S
T
2
]
;
wherein z r =z−z s (x,y,ψ),
z s ( x , y , ψ ) = 0.5 tan ψ ( x + R c - ( x + R c ) 2 + 16 ) - G sin ψ · y 4 ( y 4 + L y 4 ) - 1 ,
wherein
S T , RC = ρ 2 + ( a T , RC + ξ T , RC ) 2 ,
ξ T , RC = z r 2 + D T , RC 2 ,
D T = D 0 + δ y 2 + γ T h T ( x ) + γ 1 h 1 ( x ) ,
wherein C 1 =−98.72 when Kp=0, 0 + , C 1 =−35.64 when Kp=1 − ,1,1 30 , C 1 −77.45 when Kp=2 − ,2,2 + , C 1 =−70.12 when Kp=3 − ,3,3 30 , C 1 =−162.5 when Kp=4 − ,4,4 + , C 1 =−128.4 when Kp≧5 − ,
wherein C 2 =−10014 when Kp=0, 0 + , C 2 =−12800 when Kp=1 − ,1,1 + , C 2 =−14588 when Kp=2 − ,2,2 + , C 2 =−16125 when Kp=3 − ,3,3 + , C 2 =−15806 when Kp=4 − ,4,4 + , C 2 =−16184 when Kp≧5 − ,
wherein a T =13.55 when Kp=0,0 + , a T =13.81 when Kp=1 − ,1,1 + , a T =15.08 when Kp=2 − ,2,2 + , a T =15.63 when Kp=3 − ,3,3 + , a T =16.11 when Kp=4 − ,4,4 + , a T =15.85 when Kp≧5 − ,
wherein D 0 =2.08 when Kp=0, 0 + , D 0 =1.664 when Kp=1 31 ,1,1 + , D 0 =1.541 when Kp=2 − ,2,2 + , D 0 =0.9351 when Kp=3 − ,3,3 + , D 0 =0.7677 when Kp=4 − ,4,4 + , D 0 =0.3325 when Kp≧5 − ,
wherein R c =9.084 when Kp=0, 0 + , R c =9.238 when Kp=1 − , 1,1 + , R c =9.609, when Kp=2 − ,2,2 + , R c =8.573 when Kp=3 − ,3,3 + , R c =10.06 when Kp=4 − ,4,4 + , R c =10.47 when Kp≧5 − ,
wherein L y =10 R E ,
B x (RC) =Q RC xz r ;
B Y (RC) =Q RC yz r ;
B
Z
(
RC
)
=
C
5
2
(
a
RC
+
ξ
RC
)
2
-
ρ
2
S
RC
5
+
B
X
RC
∂
z
s
∂
x
+
B
Y
RC
∂
z
s
∂
y
-
Q
RC
D
RC
x
∂
D
RC
∂
x
;
wherein
Q RC =3C 5 ξ RC −1 S RC −5 (a RC +ξ RC )
D RC =D 0 +γ RC h RC (x)+γ 1 h 1 (x)
h T,RC =0.5[1+x(x 2 +L 2 T,RC ) −1/2 ],
h 1 =0.5{1−(x+16)[(x+16) 2 +36] −1/2 },
C 5 (Dst)=−10220+408.5·Dst
B XYZ (C) =C 3 ( F + x,y,z +F − x,y,z )+ C 4 ( F + x,y,z −F − x,y,z ),
wherein
{ F x ± F y ± } = ± W c ( x , y ) S ± [ S ± ± ( z ± R T ) ] × { x y } ,
F z ± = W c ( x , y ) S ± + ( x ∂ W c ∂ x + y ∂ W c ∂ y ) × 1 S ± ± ( z ± R T ) ,
S ± = [ ( z ± R T ) 2 + x 2 + y 2 ] 1 2 ,
W c ( x , y ) = 0.5 [ 1 - x - x 0 c [ ( x - x 0 c ) 2 + L xc 2 ] 1 2 ] × ( 1 + y 2 / D yc 2 ) - 1 ;
B X (M) =e x/Δx [C 6 z cos ψ+( C 7 +C 8 y 2 +C 9 z 2 ) sin ψ],
B Y (M) =e x/Δx [C 10 yz cos ψ+( C 11 y+C 12 y 3 +C 13 yz 2 ) sin ψ],
and
B Z (M) =e x/Δx [( C 14 +C 15 y 2 +C 16 z 2 ) cos ψ+( C 17 z+C 18 zy 2 +C 19 z 3 ) sin ψ],
wherein C 6 through C 19 are given by:
Kp C n = 0, 0 + = 1 − , 1, 1 + = 2 − , 2, 2 + C 6 1.813 2.316 2.641 C 7 31.10 35.64 42.46 C 8 −0.07464 −0.0741 −0.07611 C 9 −.07764 −0.1081 −0.1579 C 10 0.003303 0.003924 0.004078 C 11 −1.129 −1.451 −1.391 C 12 0.001663 0.00202 0.00153 C 13 0.000988 0.00111 0.000727 C 14 18.21 21.37 21.86 C 15 −0.03018 −0.04567 −0.04199 C 16 −0.03829 −0.05382 −0.06523 C 17 −0.1283 −0.1457 −0.6412 C 18 −0.001973 −0.002742 −0.000948 C 19 0.000717 0.001244 0.0002276 Kp C n = 3 − , 3, 3 + = 4 − , 4, 4 + ≧5 − C 6 3.181 3.607 4.090 C 7 47.50 51.10 49.09 C 8 −0.1327 −0.1006 −0.0231 C 9 −0.1864 −0.1927 −0.1359 C 10 0.01382 0.03353 0.01989 C 11 −1.488 −1.392 −2.298 C 12 0.002962 0.001594 0.004911 C 13 0.000897 0.002439 0.003421 C 14 22.74 22.41 21.79 C 15 −0.04095 −0.04925 −0.05447 C 16 −0.09223 −0.1153 −0.1149 C 17 −1.059 −1.399 −0.2214 C 18 −0.001766 0.000716 −0.01355 C 19 0.003034 0.002696 0.001185
and wherein L y =10.0, D x =13.0, L RC =5.0, L T =6.30, γ T =4.0, δ=0.010, γ 1 =1.0, R T =30.0, x 0c =4.0, L xc 2 =50.0, and D yc =20.0,
and thereby determining whether said particle's trajectory intersects either the boundary of earth's magnetosphere, thereby indicating an allowed trajectory, or intersecting earth's surface or earth's atmosphere, thereby indicating a forbidden trajectory.
2. The method of claim 1 , wherein said plurality of arrival directions comprises one or more randomly or pseudorandomly selected arrival directions.
3. The method of claim 1 , further comprising the step:
(D) for each particle rigidity, determine what fraction of particles of that rigidity will be transmitted to said satellite.
4. The method of claim 1 , wherein said plurality of points comprises a complete set of points for said orbit.
5. The method of claim 1 , wherein said plurality of points comprises a set of points for a portion of said orbit.
6. A method for determining, for a given particle environment outside of earth's magnetosphere, what portion of a population of particles having one or more rigidities making up said particle environment will be transmitted to a satellite in a known earth orbit, comprising the steps:
performing steps (A) through (C) of claim 1 , thereby computing a geomagnetic transmission function for said population of particles; and
applying said geomagnetic transmission function to said population of particles, thereby determining what portion of that population of particles will be transmitted to said satellite.
7. A method for determining, for a given particle environment outside of earth's magnetosphere, what portion of a population of particles having one or more rigidities making up said particle environment will be transmitted to a satellite in earth orbit, comprising the steps:
prompting a user to specify an earth orbit;
determining whether said orbit is among a group of preselected orbits, each of said orbits in said preselected group of orbits having an associated predetermined geomagnetic transmission function for a range of particle rigidities, each of said predetermined geomagnetic transmission functions having been prepared in accordance with claim 1 ; and
for the case wherein said orbit is among said preselected group of orbits, applying said predetermined geomagnetic transmission function for said orbit to said particle environment outside earth's magnetosphere.
8. The method of claim 7 , wherein said preselected group of orbits comprises a quiet shuttle orbit having a 450 km altitude and a 28.5° inclination, a disturbed shuttle orbit having a 450 km altitude and a 28.5° inclination, a quiet space station orbit having a 450 km altitude and a 51.6° inclination, and a disturbed space station orbit having a 450 km altitude and a 51.6° inclination, wherein said quiet shuttle orbit has a geomagnetic transmission function given by FIG. 4 , wherein said disturbed shuttle orbit has a geomagnetic transmission function given by FIG. 5 , wherein said quiet space station orbit has a geomagnetic transmission function given by FIG. 6 , and wherein said disturbed space station orbit has a geomagnetic transmission function given by FIG. 7 .
9. The method of claim 7 , further comprising the step:
for the case wherein said orbit is not among said preselected group of orbits, performing a step selected from the group consisting of (a) returning an error message to a user, and (b) computing a geomagnetic transmission function for said orbit, in accordance with the method of claim 1 .
10. A method for determining a flux of a species of solar ions having a specified atomic number between 3 and 92, and a specified kinetic energy, for a satellite in a near earth orbit, comprising the steps:
(A) specifying an atomic number for solar ions for evaluation;
(B) specifying a kinetic energy for said solar ions;
(C) specifying a baseline model for said flux of solar ions, wherein said baseline model is selected from the group consisting of a worst day model, a worst week model, and a peak flux model;
(D) in the case wherein said specified atomic number is greater than 20, selecting iron as an elemental spectrum model;
(E) in the case wherein said specified atomic number is less than or equal to 20, selecting oxygen as an elemental spectrum model;
(F) looking up a value for an elemental breakpoint, wherein said elemental breakpoint is a function of said elemental spectrum model and said baseline model, and wherein said elemental breakpoint is selected from the table:
Elemental Baseline model spectrum model worst day or peak flux worst week iron 24.23 MeV/nuc 19.90 MeV/nuc oxygen 15.94 MeV/nuc 12.89 MeV/nuc
(G) in the case wherein said baseline model is said worst week model, and said elemental spectrum model is iron, and said kinetic energy is greater than 127.93 MeV/nuc, calculating an unscaled flux, wherein said unscaled flux equals A sp ×(En/MeV/nuc) −Gsp , wherein A sp =3.16814×10 6 (cm 2 sr MeV/nuc) −1 , (En/MeV/nuc) is said kinetic energy, normalized to be dimensionless, and G sp =2.861;
(H) in the case wherein the condition recited in step (G) is not satisfied, and wherein said kinetic energy is greater than said elemental breakpoint, calculating an unscaled flux wherein said unscaled flux equals A 3 ×EN γsi , wherein A 3 is a function of said elemental spectrum model and said baseline model, and wherein said A 3 is selected from the table:
Baseline model Elemental worst day or peak flux worst week spectrum model in (cm 2 sr MeV/nuc) −1 in (cm 2 sr MeV/nuc) −1 iron 0.252948 × 10 10 0.249719 × 10 9 oxygen 0.106702 × 10 10 0.667628 × 10 9
and wherein γ si is a spectral index and is a function of said elemental spectrum model and said baseline model, and wherein said γ si is selected from the table:
Elemental Baseline model spectrum model worst day or peak flux worst week iron −4.52970 −3.7610 oxygen −4.14060 −3.76850
(I) in the case wherein the condition recited in step (G) is not satisfied, and wherein said kinetic energy is less than or equal to said elemental breakpoint, calculating an unscaled flux wherein said unscaled flux equals A 2 exp(−G×En 1/4 )×En 1/4 , wherein A 2 is a function of said elemental spectrum model and said baseline model, and wherein said A 2 is selected from the table:
Baseline model Elemental worst day or peak flux worst week spectrum model in (cm 2 sr MeV/nuc) −1 in (cm 2 sr MeV/nuc) −1 iron 1.8991 × 10 8 3.0372 × 10 8 oxygen 4.9518 × 10 8 1.1307 × 10 9
and wherein G si is a spectral index and is a function of said elemental spectrum model and said baseline model, and wherein said G si is selected from the table:
Elemental Baseline model spectrum model worst day or peak flux worst week iron 5.70 5.70 oxygen 5.70 5.70
; and
(J) in the case where said atomic number is between 3 and 92, inclusive, calculating a solar ion flux for said specified atomic number and said specified kinetic energy by multiplying said unscaled flux by a scale factor ratio, said scale factor ratio being the ratio of a scale factor for an element having said selected atomic number over a scale factor for said spectrum model element, wherein said scale factors are selected from the table:
Atomic Number Scale Factor 5 0 6 4.704 × 10 −1 7 1.2059 × 10 −1 8 1 9 4.560976 × 10 −5 10 2.1312 × 10 −1 11 1.744715 × 10 −2 12 2.0624 × 10 −1 13 1.826829 × 10 −2 14 3.5935 × 10 −1 15 2.279675 × 10 −4 16 9.758 × 10 −2 17 1.680488 × 10 −4 18 1.771545 × 10 −3 19 3.644715 × 10 −4 20 4.826 × 10 −2 21 2.929 × 10 −4 22 4.377 × 10 −3 23 4.088 24 1.65 × 10 −2 25 5.625 × 10 −3 26 1 27 1.303 × 10 −2 28 3.172 × 10 −2 29 3.048 × 10 −4 30 7.457 × 10 −4 31 4.878 × 10 −5 32 1.22 × 10 −4 33 7.317 × 10 −6 34 7.317 × 10 −5 35 9.756 × 10 −6 36 4.878 × 10 −5 37 7.317 × 10 −6 38 2.439 × 10 −5 39 4.878 × 10 −6 40 1.22 × 10 −5 41 9.756 × 10 −7 42 4.878 × 10 −6 43 0 44 2.195 × 10 −6 45 4.878 × 10 −7 46 1.463 × 10 −6 47 4.878 × 10 −7 48 1.707 × 10 −6 49 2.195 × 10 −7 50 4.878 × 10 −6 51 3.415 × 10 −7 52 7.317 × 10 −6 53 1.463 × 10 −6 54 6.585 × 10 −6 55 4.878 × 10 −7 56 4.878 × 10 −6 57 4.878 × 10 −7 58 1.22 × 10 −6 59 1.951 × 10 −7 60 9.756 × 10 −7 61 0 62 2.439 × 10 −7 63 9.756 × 10 −8 64 4.878 × 10 −7 65 7.317 × 10 −8 66 4.878 × 10 −7 67 9.756 × 10 −8 68 2.439 × 10 −7 69 4.878 × 10 −8 70 1.951 × 10 −7 71 4.878 × 10 −8 72 1.951 × 10 −7 73 2.195 × 10 −8 74 2.439 × 10 −7 75 4.878 × 10 −8 76 7.317 × 10 −7 77 7.317 × 10 −7 78 1.463 × 10 −6 79 2.439 × 10 −7 80 2.439 × 10 −7 81 2.195 × 10 −7 82 2.439 × 10 −6 83 1.463 × 10 −7 84 0 85 0 86 0 87 0 88 0 89 0 90 4.878 × 10 −8 91 0 92 2.927 × 10 −8 3 0 4 0
wherein elements having atomic number of 20 or less are scaled to oxygen, and elements having higher atomic numbers are scaled to iron.
11. A method for determining a flux of solar ions of species having a range of atomic numbers between 3 and 92, wherein each of said species includes particles having a range of specified kinetic energies, for a satellite in a near earth orbit, comprising the steps:
(A) for each kinetic energy of each of said species, performing steps (A) through (K) of claim 10 , and storing a flux value for each of said kinetic energies for each of species; and
(B) adding each of said flux values to obtain a total solar ion flux value.
12. A method for modeling the effects of cosmic rays on microelectronics on a computer connected to the internet, comprising the steps:
(A) receiving a login message from a remote user connected to the internet, and generating and transmitting back to said user with a script in response thereto an HTML main menu page, wherein said main menu page comprises prompts for said user to run one or more routines selected from the group consisting of: (1) a routine for calculating a geomagnetic transmission function for SEU-inducing particles, (2) a routine for calculating a flux of SEU-inducing particles in the near earth environment or in the environment shielded by earth's magnetosphere, (3) a routine for calculating a solid shielding transport function for SEU-inducing particles, (4) a routine for calculating a proton induced single event upset rate, (5) a routine for calculating a linear energy transfer rate, and (6) a routine for calculating a heavy ion induced single even upset rate, said main menu page futher comprises prompts for said user to select a user request file for each of said routines;
(B) in response to a message from said user to run at least one of said routines, using a user request file specified by said user, generating and executing with a script a system command for said computer to run each of said specified routines; and
(C) in response to the completion of all of said routines specified by said user, generating and transmitting to said user with a script an HTML page notifying said user of said completion.
13. The method of claim 12 , wherein said main menu page generated and transmitted to said user further comprises prompts for said user to create or edit a user request file for any one of said routines, in lieu of running said one or more of said routines, and further comprising the step:
(D) in response to a message from said user to create or edit a user request file, generating and transmitting to said user with a script an HTML page with prompts for the entry of fields for said user request file; and
(E) in response to said user transmitting information for said user request file, storing said information in a user request file with a script.Cited by (0)
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