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