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Database for Imaging and Transport withEnergetic Neutral Atoms (ENAs)
Nicholas Lewkow
Harvard-Smithsonian Center for AstrophysicsUniversity of Connecticut
April 26, 2013
CollaboratorsVasili Kharchenko[1,2]
Peng Zhang[3] Marko Gacesa[4]
Brad Snios[2] Michael Winder[2]
Daniel Violette[2] Joshua Squires[2]
[1] Harvard-Smithsonian CfA[2] University of Connecticut
[3] Duke University[4] Max Planck Institute
Introduction
Energetic neutral atoms (ENAs) aresignificantly more energetic than localthermal environment
Planetary atmosphere E ∼ 0.01 eVLocal interstellar cloud E ∼ 0.1 eVLocal interstellar bubble E ∼ 100 eV
ENAs result from charge exchange (CX)collisions between hot ions and neutralgases
Produced in any environment with hotplasma and cold gas
Solar wind (SW) ionsMagnetospheric ions
)DVW,RQ (QHUJHWLF1HXWUDO
6ORZ1HXWUDO 6ORZ,RQ
Earth ENAs
(Brandt et al., 2005)
Mars ENAs
(Brinkfeldt, et al., 2005)
Titan ENAs
(Brandt et al., 2005)
Introduction
IBEX full sky map (McComas et al., 2009)
ENAs offer a way to image space plasmasNo interaction with magnetic fieldsPlasma velocity during creation ismaintained through ENAs
ENAs may be a large source of energydeposition in astrophysical environments
Precipitation of ENAs in planetaryatmospheres induce atomic escape fluxes
Parameters needed for accuratemodeling
Energy transfer/relaxation ratesCollision induced emissions andreactionsProduction rates of secondary hotatoms (SHAs)Transport/thermalization ratesEnergy balance in astrophysicalsystems
Accurate quantum mechanical (QM) cross sections needed to study interactionbetween ENAs and astrophysical environments
Atomic Collisions: Database
Database for atomic/molecularcollisions in astrophysicalenvironments
Energy relaxation governed bycollisional dynamicsRequire energy-angulardependent cross sections
Collision energy 0.01 eV-10 keVInelastic channels not consideredin current energy interval
Current QM elastic atom-atomcross sections
H+HHe+HHe+HeHe+O
0 2000 4000 6000 8000 10000CM Collision Energy [eV]
0
1×104
2×104
3×104
4×104
Nu
mber
of
Par
tial
Wav
es
H+H
He+H
He+He
He+O
Number of partial waves needed for convergence of
scattering amplitude f(θ)
Asymptotic wavefunction Scattering Amplitude DCS
ψ(r →∞) ∼ eikz+f(θ)eikr
rf(θ) =
1
k
∞∑l=0
(2l+1)eiδl sin δlPl(cos θ)dσ
dΩ= |f(θ)|2
Atomic Collisions: Differential Cross Sections
He+He
0 0.1 0.2 0.3 0.4 0.5Lab Scattering Angle [deg]
104
105
106
107
108
Dif
fere
nti
al C
ross
Sec
tion [
a0
2]
0.5 keV (x100)
1.5 keV (x10)
5.0 keV
Expt: Nitz et al. (1987)
He+H
0 0.1 0.2 0.3 0.4 0.5Lab Scattering Angle [deg]
103
104
105
106
107
108
Dif
fere
nti
al C
ross
Sec
tion [
a0
2]
0.5 keV (x100)
1.5 keV (x10)
5.0 keV
Expt: + → Gao et al. (1989) o → Newman et al. (1986)
QM cross sections compared withavailable laboratory data
Semi-classical Eikonal method alsocompared with QM results
δ(ρ) =−1
2~v
∫ ∞−∞
U(√
ρ2 + z2)dz
f(θ) = −ik∫ ∞0
[e2iδ(ρ) − 1
]J0(kθρ)ρ dρ
He+O
0 0.1 0.2 0.3 0.4 0.5Lab Scattering Angle [deg]
104
105
106
107
108
109
1010
Dif
fere
nti
al C
ross
Sec
tio
n [
a0
2]
0.5 keV (x100)
1.0 eV
1.5 keV (x10)
5.0 keV
Expt: + → Smith et al. (1996) o → Schafer et al. (1987)
Atomic Collisions: Total Cross Sections
Total elastic cross section σEL(E)Cross sections available for several smallenergy intervalsNo cross sections available over entireinterval meV - keV
σEL(E) =
∫|f(θ, E)|2 dΩ
Total diffusion cross section σDF (E)Useful for energy-momentumtransfer without solving Boltzmannequation
σDF (E) =
∫|f(θ, E)|2 (1− cos θ) dΩ
10-1
100
101
102
103
104
CM Collision Energy [eV]
101
102
Tota
l C
ross
Sec
tion [
a 0
2]
10-2
10-1
100
100
150
200
250
300
350
He+H
4He+
3He
He+O
4He+
4He
3He+
3He
H+H
10-2
10-1
100
101
102
103
104
CM Collision Energy [eV]
10-3
10-2
10-1
100
101
102
Dif
fusi
on
Cro
ss S
ecti
on
[a
0
2]
He+O
H+H
He+H
He+He
Atomic Collisions: Probability Densities
Probability Density Normalized Cumulative Probability
ρ(E, θ) =2π sin θ
σ(E)|f(E, θ)|2
∫ π
0
ρ(E, θ) dθ = 1 P (E, θ) =
∫ θ
0
ρ(E, θ′) dθ′
He+He
Sca
tte
rin
g A
ng
le (
de
g)
0 50 1000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2He+H
Collision Energy (eV)0 50 100
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2He+O
0 50 1000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
10
20
30
40
50
60
He+H collisions
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
Lab Scattering Angle [deg]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
P (
E,θ
)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1 -
P (
E,θ
)
5.0 keV
1.5 keV
0.5 keV
0.018 deg
0.050 deg
0.120 deg
Extremely forward peaked!
Several collisions to thermalizeVery little momentum transferred per collision
Atomic Collisions: Thermalization
10-2
10-1
100
101
102
103
104
Collision Energy [eV]
0
0.5
1
1.5
2
2.5
Av
erag
e E
ner
gy
Lo
ss P
er C
oll
isio
n [
eV]
He+H
He+He
He+O
H+H
< δE >= E2mpmt
(mp +mt)2
(σDF (E)
σEL(E)
)2000 4000 6000 8000 10000
Final Energy [eV]
102
103
104
105
Num
ber
of
Coll
isio
ns
H+HHe+H
He+HeHe+O
N (Ei, Ef ) =
∫ Ei
Ef
dE
< δE >
Atom-Molecule Collisions
Many atmospheres havesignificant molecularconstituents
Accurate QM atom-moleculecross sections extremelydifficult to calculate
Complex potential surfacesLots of scattering channels
Empirical scaling methods maybe used for unknownatom-atom, atom-moleculecollisions
Model Martian Atmosphere
Krasnopolsky, 2002.
Atom-Molecule Collisions: Reduced Coordinates
Lewkow et al., 2012.
Reduced energy coordinates
ρ = θ sin θ|f(E, θ)|2 τ = Eθ
Reduced velocity coordinates
ρ = θ sin θ|f(E, θ)|2 τ =Eθ
µ
Universal amplitude fit
|f(E, θ)|2 =exp
[A (log τ)2 +B log τ + C
]θ sin θ
A = −0.13 B = 1.0 C = 2.7
Atom-Molecule Collisions: Universal Amplitude
Scaled atom-molecule cross sections
102
103
104
E θ / µ [eV deg/u]
101
102
θ s
in θ
| f(
E,θ
) |2
[
deg
a0
2]
Universal Amplitude
O+CO2
He+O2
H+O2
Quantum He+X
O+CO2 collision 1.5 keV lab frame
0 1 2 3 4 5 6 7 8CM Scattering Angle [deg]
102
103
104
105
Dif
fere
nti
al C
ross
Sec
tion [
a0
2]
Universal Amplitude
Expt (Smith et al., 1996)
Atom-molecule cross sections require a scaling of ρ to match atom-atom crosssections and the universal amplitude curve
ρ(E, θ)→ ρ(E, θ)
λwhere λ = 1.4
ENA Production
Simple models usedNo magnetic SWstreamlines usedNo SW ion energy loss
Nsw → Ion density at R0
usw → SW velocity at R0
σcx → CX cross sectionn→ neutral density
Solar wind flux density
Jsw(R) = NswuswR2
0
R2exp
(−∑i
∫ ∞R
σcxi ni(R′) dR′
)ENA production rate
q(R) = Jsw(R)∑i
σcxi ni(R)
Interstellar Medium
10-16
10-15
10-14
10-13
10-12
10-11
10-10
ENA Production [cm-3
s-1
]
0
200
400
600
800
1000
Dis
tan
ce f
rom
Su
n [
AU
]
Hydrogen
Helium
Target gas: H and HeHomogeneous distribution
Martian Atmosphere
10-4
10-3
10-2
10-1
100
101
ENA Production [cm-3
s-1
]
200
400
600
800
1000
1200
Alt
itude
[km
]
Hydrogen
Helium
Target gas: H, He, O, and CO2
Non-homogeneous distribution
Transport: Martian Atmosphere
Monte Carlo transport
ENA Created
SHA Created
ENA CreatedENA Escape
Thermalize
Thermalization height
0 1 2 3 4 5 6 7
x 10−5
80
90
100
110
120
130
140
150
160
170
180
Normalized Frequency
Altitu
de
[km
]
0 10 20 30 40 50 60 70 80 90Solar Zenith Angle [deg]
0
20
40
60
80
100
Per
cen
tag
e o
f E
nse
mb
le Escape
Thermalize
0 0.2 0.4 0.6 0.8Average Energy Loss per Collision [eV]
80
100
120
140
160
180
200
Alt
itude
[km
]
106 particle ensemble
103-105 collisions to thermalize
∼ 200 SHAs created per ENA
Transport: Interstellar Medium
Local bubbleT = 106 K (86 eV)Low density, ∼95% ionized
Local cloudsT = 6000 K (0.5 eV)High density, ∼25% ionized
ENAs may have largedisplacements duringthermalization
Helium ENAs thermalizefaster than hydrogen ENAs
More energy transferredper collision
Vergley et al., (2001) Frisch et al., (2011)
Distance from Star [LY]
ENA
Ener
gy [e
V]
0 5 10 15 20 250
2000
4000
6000
8000
10000
12000
Log 10
Per
cent
Ens
embl
e
−8
−7
−6
−5
−4
−3
−2
−1
0
050100150200
01000
20003000
0
1
2
3
4x 104
Energy [eV]Displacement [LY]
Num
ber o
f Col
lisio
ns
HHe
Conclusions
ENAs offer a way to image remote space plasmas
Accurate modeling of interactions between ENAs and astrophysicalenvironments requires angular-energy dependent cross sections
Database of QM atomic collisionsH+HHe+HHe+HeHe+OCollision energies 0.01 eV - 10 keV
Empirical model for unknown atom-molecule collision developed
Newly computed database used in transport of ENAs in interstellarmedium and Martian atmosphere
Forward peaked QM cross sections require several collisions and largedisplacements before thermalization