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D. Seckel, Univ. of Delaware
Apr 9, 2005
Scaling of Askaryan Pulses
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Topics
• RF pulses from Showers
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Radiation from single particles
ZHS: 2
0.5
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E iEi iSin 3 x t x, tei , x
Sum over particles/Integrate over shower
Shower Front + Light Cone
i t
Density of Excess Projected Track Length
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Separation of Variables & Form Factor
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Phase Factors and Rescaling FF
Most MC’s use this
z 2 c
zsin tan c 1 cos 2 c
z tan c
y 2 c
ytan ccos sin 2 cy tan c
Gy, y f yyeiy,, y, z y f yyei ayy; ay 2
ctan ccos sin
Gy0, ay GyayGz, Gzaz; az 2
csin tan c 1 cos
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Normalization and Determination of f, Gy, Gz
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AVZ, ZHS, (G4 later)
E, 0, ice 2.53 107 0 1
1.01.44 ,
Gy 1
1.01.44 , f0 2.53 107
0Sinc0 (units?).
AVZ Use a Gaussian, and give the half-width of the Cerenkov cone at 1 GHz as 3.72 ° for a 1 PeV (3.1 m) shower.
Determine Gz as FT of gaussian
0 0.5 1 1.5 2 2.5 3nu
0
0.2
0.4
0.6
0.8
1
G y
Gy avz black , zhs red
0 0.05 0.10.15 0.20.25 0.3nu
0
0.2
0.4
0.6
0.8
1G z
Gz avz black , zhs red
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Scaling vs AVZ
Field calculation is integral over shower profile
Separation of shower profile
Separation of form factors
With scaled frequencies• Adapted from Alvarez, Vazquez, Zas• “Full sim” is approx a
• Blue – Gaussian for f(z), AVZ approx c for Gy
• Red – Griessen for f(z)
Separation of phase factors
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High frequency
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Phases
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Scaling with energy and type
Comparison of em and hadronic shower length
-2 0 2 4 6 8LogEPeV1
1.5
2
2.5
3
hslhsl me
VeP
-2 0 2 4 6 8LogEPeV0
0.25
0.5
0.75
1
1.25
1.5
goLhsl
hslmeVeP
f0 : l tot E
d EdxGy : Rm doesn't change
Gz : lshi, E
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Scaling with medium
AVZ scaled
G4
f0 : l tot iE
d EdxGy : RM
Esd Edx
Gz : lsh x X
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Scaling behavior
fractional excess
Single particle & shower signals
Includes LPM effect
z
y
c
to observer
ivt
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Pulse shapes
-6 -4 -2 0 2 4 6
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
-4 -2 0 2 4tns-400
-200
0
200
400
EVmc
f0avz ,gyavz ,gzavz ,phisavzeev : 0.01d: 2.r: 0.00001
dnu : 0.02nu0 : 20.48mat : icetype : em
0.25 0.5 0.75 1 1.25 1.5 1.75 2GHz0
0.1
0.2
0.3
0.4
0.5
0.6
1
0001xE
Vmc
zHG E:black , Gy:red , Gz:blue , Gatt:green
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Scaling model w/Shahid’s G4 10 TeV shower
-4 -2 0 2 4tns-400
-300-200-100
0100200300
EVmc f0sh ,gysh ,gzsh ,phisavzeev : 1d: 2.r: 1
dnu : 0.02nu0 : 5.12mat : icetype : em
-4 -2 0 2 4tns-100
-50
0
50
EVmc f0sh ,gysh ,gzsh ,phisavz
eev : 1d: 4.r: 1
dnu : 0.02nu0 : 5.12mat : icetype : em
-4 -2 0 2 4tns-50
0
50
100
EVmc f0sh ,gysh ,gzsh ,phisavz
eev : 1d: 4.r: 1
dnu : 0.02nu0 : 5.12mat : icetype : em
-4 -2 0 2 4tns-300
-200-100
0100200300
EVmc f0sh ,gysh ,gzsh ,phisavz
eev : 1d: 2.r: 1
dnu : 0.02nu0 : 5.12mat : icetype : em
-4 -2 0 2 4tns-750
-500-250
0250500750
EVmc f0sh ,gysh ,gzsh ,phisavz
eev : 1d: 0.r: 1
dnu : 0.02nu0 : 5.12mat : icetype : em
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Multiple showers
-4 -2 0 2 4tns-0.000075
-0.00005
-0.000025
0
0.000025
0.00005
0.000075EVmmc
Comparison of RF signal from split shower blackto original redSeparation of 4. m, distance 1km, d 4°, e 1
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Fluctuations
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Better shower profiles?
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Acoustic (in progress)
• Same as radio except– scalar vs vector– total track length– v/c is smaller– attenuation– experiment bandwidth
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Summary
