Magnetic & Acoustic Waves in the Aurora

Jada Maxwell

Photo: Michael KlenschCourtesy of http:www.nordlys.com

Can magnetic waves in the aurora transform into acoustic waves?

Magnetic Waves

Earth

Transform into Sound Waves

Earth

Alfvén waves (s-mode)

Magnetosonic (like acoustic waves=p-mode)

Types of Magnetic Waves

Images courtesy of Georgia State Universityhttp://hyperphysics.phy-astr.gsu.edu/hbase/sound/tralon.html

BBC animations

0

quantity intertial

force restoring

BV

m

TkC

TV

A

iS

string

Velocity of Waves

B

G

A

S

P

P

V

C 2

22

Beta

Plasma is like Rubber Bands in Jello

DominatesNeither 1

Bands)(Rubber Dominates Pressure Magnetic 1

(Jello) Dominates Pressure Gas 1

B

G

G

B

P

PB

G

P

P

P

P

Location Altitude (km)

Fairbanks, Ak 120

Seattle, Wa 120

Equator 150

Where Does Beta=1?

Image courtesy of http://en.wikipedia.org/wiki/Image:Atmosphere_model.pngGraph made from data obtained at http://uap-www.nrl.navy.mil/models_web/msis/msis_home.htm

Earth’s Atmosphere

Calculating Magnetic Pressure (PB)

3

00

3

00

22

)sin(

)cos(2

r

rBB

r

rBB

BBB

r

r

0

2

2B

PB

Calculating Gas Pressure (PG)

J/K1038.1

massion m

density mass

density particle

23

i

xk

mn i

nkTPG

Calculating Velocity of Acoustic Waves (CS)

iS m

TkC

gas idealan in heats specific of ratio3

5

Calculating Velocity of Alfvén Wave (VA)

0

BVA

Data Rearth Surface magnetic fieldr0(m) B0(G) B0(T)6.40E+06 0.47 4.70E-05

alt(km) alt(km) alt(km) alt(km) alt(km)50 70 90 120 150

r0 r(m) r(m) r(m) r(m) r(m)lat th(deg) th(rad) 6.40E+06 6.45E+06 6.47E+06 6.49E+06 6.52E+06 6.55E+06

Fairbanks, AK 64 26 0.453556

theta component of field = B0 sin(th) (r0/r)^3 = B_th 2.06E-05 2.01E-05 1.99E-05 1.97E-05 1.95E-05 1.92E-05radial component of field = 2 B0 cos(th) (r0/r)^3 = B_r 8.45E-05 8.25E-05 8.18E-05 8.10E-05 7.99E-05 7.88E-05

Total magnetic field = SQRT(Br^2 + Bth^2) = B 8.70E-05 8.50E-05 8.42E-05 8.34E-05 8.23E-05 8.11E-05Magnetic pressure = B^2/(2*mu_0)= PB 3.01E-03 2.87E-03 2.82E-03 2.77E-03 2.69E-03 2.62E-03

mass density(kg/m3)= rho 1.00E+00 1.00E-03 1.00E-04 4.00E-06 1.00E-08 2.00E-09particle density = rho/m_ion = n 4.27E+25 4.27E+22 4.27E+21 1.71E+20 4.27E+17 8.53E+16

temperature = T(K) 2.75E+02 2.75E+02 2.25E+02 1.50E+02 4.00E+02 7.30E+02Gas pressure = nkT = Pg 1.62E+05 1.62E+02 1.33E+01 3.54E-01 2.36E-03 8.60E-04

mks Alfven speed =B*SQRT(1/(mu_0*rho)) = vA 7.76E-02 2.40E-03 7.51E-04 1.49E-04 7.34E-06 3.24E-06mks sound speed=SQRT(gam*T*k/mN) = cs 5.20E+02 5.20E+02 4.70E+02 3.84E+02 6.27E+02 8.47E+02

mks plasma beta = Pg/PB = beta 5.38E+07 5.64E+04 4.70E+03 1.28E+02 8.75E-01 3.28E-01

Constants:pi= 3.14

Tesla= 1.00E+04 Gaussmu_0= 1.26E-06 T.m/A

rad= 57.32484 degBoltzmann k= 1.38E-23 J/K

g/cm3= 1.00E+03 kg/m3proton mass mp= 1.67E-27 kg

Nitrogen mass mN= 2.34E-26 kggamma= 1.667

Calculations for Fairbanks, Ak

Location Altitude (km)

Fairbanks, Ak 120

Seattle, Wa 120

Equator 150

Where Does Beta=1?

• How does atmospheric heating from auroral processes affect Beta?

• At what frequencies do these waves occur?

• How much does wave transformation contribute to infrasound compared with the gas expansion theory?

More Questions to Investigate

Sources:

• Thanks to Dr. E.J. Zita for her guidance and helpful discussions

• Johnson, M.C., Petty-Powell, Sarah and Zita, E.J., ‘Energy Transport by MHD Waves Above the Photosphere Numerical Simulations,’ 17 Oct 2002

• Michael KlenschCourtesy of http:www.nordlys.com

• http://en.wikipedia.org/wiki/Image:Atmosphere_model.pngGraph made from data obtained at http://uap-www.nrl.navy.mil/models_web/msis/msis_home.htm

• Georgia State Universityhttp://hyperphysics.phy-astr.gsu.edu/hbase/sound/tralon.html

http://academic.evergreen.edu/m/maxjad02