Apr 9, 2005 Scaling of Askaryan Pulses D. Seckel, Univ. of Delaware.

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