Calculation of the Alfvén Radius from Observations at 1 AUBrandon Ng, Colonie Central High School, Albany, NY

Advised by: Charles W. Smith and Molly Goelzer c... Program code8.for ........................................cc Routine to read OMNI2 data and output select values.cc..............................................................c

implicit noneinteger*2 ipt, iF1aver, iNpaver, iVswaver, iMAaver, icountinteger*4 iyear, iday, ihour, iBartelsinteger*4 imf_id, plasma_id, npts_imf, npts_plasmainteger*4 iBartels_lastinteger*4 ii, iwholereal*4 F1, F2, imf_lat, imf_lonreal*4 Bx_gse, By_gse, Bz_gse, By_gsm, Bz_gsmreal*4 F1_aver, Np_aver, Vsw_aver, MA_averreal*4 sigma_F1, sigma_F2, sigma_Bx, sigma_By, sigma_bz, Tp, Np, Vswreal*4 V_long, V_lat, NaNp, NV2

real*4 sigma_T, sigma_N, sigma_V, sigma_V_long, sigma_V_latreal*4 sigma_ratio, Efield, beta, MAreal*4 F1_bad, Tp_bad, Np_bad, Vsw_bad, MA_badreal*4 pi, twopi, RS, AU, omegareal*4 denom, R0, B0, Np0, VA0, R, BatR, NpatR, VAatRreal*4 R_old, R1, R2, VA_old, VA1, VA2real*4 Tex, VA_avercharacter*14 idget

cF1_bad = 999.9Tp_bad = 9999999.Np_bad = 999.9Vsw_bad = 9999.MA_bad = 999.9

cpi = 4.*atan(1.)twopi = 2.*piRS = 6.955E+5AU = 1.496E+8omega = twopi / (26.0 * 24.0 * 60.0 * 60.0)

cwrite(6,*)' 'write(6,*)' Program code8.for uses input data'write(6,*)' and outputs VA solutions.'write(6,*)' Do you want to output whole functions? (1 = yes)'read(5,*)iwhole

copen(unit=14, file='code8.dat', form='formatted', status='unknown')

cF1_aver = 0.0Np_aver = 0.0Vsw_aver = 0.0MA_aver = 0.0

cwrite(6,*)' Input field strength [nT], density [cm^-3]

and wind speed [km/s] at 1 AU:'read(5,*) F1_aver, Np_aver, Vsw_averVA_aver = 21.8 * F1_aver / sqrt(Np_aver)MA_aver = Vsw_aver / VA_averwrite(6,*) F1_aver, Np_aver, Vsw_aver

cc... compute new stuff (take everything back to 2 RS):

denom = 1. + (omega * AU / Vsw_aver)**2 denom = sqrt(denom) R0 = 2.*RS B0 = (F1_aver / denom) * ((AU / R0)**2) write(6,*)' Assuming R0 = 2RS, B0 = ', B0 write(14,*)' Assuming R0 = 2RS, B0 = ', B0 Np0 = Np_aver * ((AU / R0)**2) write(6,*)' Assuming R0 = 2RS, Np0 = ', Np0 write(14,*)' Assuming R0 = 2RS, Np0 = ', Np0 VA0 = 21.8 * B0 / sqrt(Np0) write(6,*)' Assuming R0 = 2RS, VA0 = ', VA0 write(14,*)' Assuming R0 = 2RS, VA0 = ', VA0

c R_old = R0 VA_old = VA0 do 1800 ii=1,500 ! evolve out to greater distances R = R0 + float(ii)*0.5*RS BatR = B0 * ((R0/R)**2) * sqrt(1. + ((omega*R/Vsw_aver)**2)) NpatR = Np0 * ((R0/R)**2) VAatR = 21.8 * BatR / sqrt(NpatR) if((VA_old .gt. Vsw_aver) .and. (VAatR .lt. Vsw_aver)) then

VA1 = VA_old VA2 = VAatR R1 = R_old R2 = R write(6,*) ' VA crosses Vsw between:' write(6,1740) ii-1, R1, R1/RS, VA1 write(6,1740) ii, R2, R2/RS, VA2 write(14,*) ' VA crosses Vsw between:' write(14,1740) ii-1, R1, R1/RS, VA1 write(14,1740) ii, R2, R2/RS, VA2

1740 format(2x,' ii, R, R/RS, VA at R = ',i3,3(2x,1pe11.4)) endif R_old = R VA_old = VAatR if(iwhole .eq. 1) then

write(6,1750) ii, R, R/RS, VAatR, BatR, NpatR write(14,1750) ii, R, R/RS, VAatR, BatR, NpatR

endif 1750 format(2x,' ii, R, R/RS, VA at R, B at R, Np at R = ',i3,5(2x,1pe11.4)) 1800 continuec

close(unit=14)stopend

Figure 1. Crossing Distance vs. Magnetic Field Strength shows a direct relationship.

Figure 2. Crossing Distance vs. Solar Wind Speed displays an indirect relationship.

Figure 3. Crossing Distance vs. Proton Density illustrates the inverse relationship.

Figure 4. This graph contains figures 1,2, and 3 showing the effects of each.

Figure 5. This graph is an example of how magnetic field strength, proton density, and solar wind speed affect the alfven radius as a whole.

Introduction:

The Helios-A and Helios-B spacecrafts were launched on December 10, 1974, and January 15, 1976, respectively. These solar probes made it .29 AU, or approximately 62 Rʘ (solar radii), away from the sun. There are many questions NASA wants to answer relating to the sun such as coronal mass ejection or solar wind acceleration, but to approach the sun any closer, the determination of the alfvén radius is needed. This is the point when the alfvén speed equals the solar wind speed. A program was written to achieve this.

Methods:

A program was made to output good data and toss out bad data. These outputs included alfvén speed, solar wind speed, proton density, and magnetic field strength. Graphs were then created to show the point of intersection between VA and Vsw; this point was considered the alfvén point or radius. Another program was created to test each individual factor and its effect on the alfvén radius. All other factors were held constant to show the general trend.

Results:

General trends can be seen in figures 1,2,3, and 4; however, because these factors frequently change, the alfvén radius alters. Even the slightest change affects the radius.

Conclusion:

A program was written to determine the alfvén radius using data collected at 1 AU. This program can be used for further study in NASA’s solar probe expedition scheduled for 2018. The probe will be expected to come within 10 Rʘ from the sun and will be the first spacecraft to enter the atmosphere of the sun.