Monte Carlo simulation of radio pulses in atmospheric

Monte Carlo simulation of radio pulses inatmospheric showers using ZHAireS

Jaime Alvarez-Muniz

Washington Rodrigues de Carvalho Jr.

Enrique Zas

University of Santiago de Compostela

Radio Simulations for Neutrino and Cosmic Ray Detectors

The Ohio State University

February 23, 2012

Monte Carlo simulation of radio pulses in atmospheric showe rs using ZHAireS – p. 1

The ZHAireS code

ZHAireS (ZHS + Aires): New simulation of radio emissionin air showers (Also works in dense media)(AstropaPhys, 35,325, 2012)

Full shower simulation using Aires

Radio emission calculation based on ZHS algorithms(Zas, Halzen, Stanev, Phys.Rev.D V45, 362 (1992) and Phys.Rev.D81:123009,2010)

First principles (Maxwell) - No emission model presuposed.(Geomagnetic, Charge Excess (Askaryan), etc... all included)

Frequency- and Time-domain calculations of vectorpotential ~A and electric field ~E

Takes into account varying refraction index n(h)

Offline integration


AIRES

Well known and widely used EAS simulation software

primaries: p, e±, γ, nuclei, etc... (even ν as special primary)

All relevant EM processes included (including LPM)

All relevant low energy hadronic processes included

External HE models: QGSJET, QGSJETII and SYBILL

Curved Earth, US Standard Atmosphere, etc...Very good agreement with CORSIKA, but usually faster


Thinning level comparison

ZHS uses “sandwich” thinning: Thinning only for particles

between Emax and Emin (AstroparPhys 32, 100, 2009)

ZHAireS mimics ZHS by using a very low maximum weight.

Default Parameters: Eth = 10−4E0 and Weight factor Wf = 0.06

The maximum weight is then Wr = 14GeV −1 · Eth ·Wf

Using Eth = 10−5E0 increases runtime more than 8 fold!

2:30h with default parameters (single processor, shower 4 with 64 antennas)

Time (ns)0 10 20 30 40 50 60

E (

V/m

)

0

0.1

0.2

0.3

0.4

-310×

-5Thinning 10-4Thinning 10

(Mhz)ν1 10 210

E (

V/m

/MH

z)

-710

-610-5Thinning 10-4Thinning 10


Time and frequency domains

Time domain~A(t, u) = µe

4πRc~β⊥

Θ(t−tdet1 )−Θ(t−tdet2 )

1−n~β·u

Frequency domain~E(ω, u) = − µe

2πc~β⊥

eiω(t−tdet1 )−eiω(t−tdet2 )

1−n~β·u

û (const)

R v (const)

t1,E1,x1

t2,E2,x2

θ

. (Phys.Rev.D81:123009,2010)

-4 -3 -2 -1 0 1 2 3 4 5-2

-1

0

1

2

3

4

5

6

A(x,t)

(arb

. unit

s)

� >� C

(1� n� cos� )(t2 � t1 )

� ec� sin�

4� (1� n� cos� )

� < � C

� � � C

-4 -3 -2 -1 0 1 2 3 4 5

t� nR/c (arb. units)-6

-4

-2

0

2

4

6

E(x,t)

(arb

. unit

s)

� >� C� < � C

� � � CE= � dA/dt


Model for the variation of n with height

Refractivity R(h)R(h) = [n(h)− 1]× 106 = Rs exp (−Krh),

where Rs = R(h = 0) = 325 and Kr = 0.1218 km−1

Reproduces published values for R(h) up to 20km within 1% (including humidity)

Effective refractive index neff for each particle track:

Used for the calculation of the retarded times tdet

neff = 1 +Reff × 10−6,

where Reff = 1R

∫ R

0 R(h) dl

R

h


Reff : Curved earth vs flat approximation

Flat earth case: Big errors for large zenithal angles

Curved Earth case: Full integral calculation too expensive

Curved Earth Approximation: Divide integral into N pieces:

Reff =1

R

∫ R

0R(h) dl → Reff =

1

R

N∑

i=0

∫ Pi+1

Pi

R(h) dli (1)

h0

h1

h2

h3

h4

hdet

h0

z

α0

R0

R (km)0 100 200 300 400 500 600 700

Err

or (

%)

eff

R

-110

1

10 °85

°80

°75°70

°60


Curved vs Flat Earth neff calculation

Time (ns)10 20 30 40 50 60 70 80

E (

V/m

)

0

0.02

0.04

0.06

0.08

-310×

effCurved Earth n

effFlat approximation n

°=70θ

Time (ns)140 160 180 200 220 240 260

E (

V/m

)

-2

0

2

4

6

8

10

12

14

16

-610×

effCurved Earth n

effFlat approxinmation n

°=88θ


Toymodel: retarded times

hR

r

show

er a

xis

antennat=0e

t= -hc

e

Detection (retarded) time:

tdet = n√h2+r2−h

c

For n>1 pulse begins at:

tdetmin = r√n2−1c

Related with an altitude:

htmin = r√

1(n2−1)


Prominent role of geometry in radio emission

n = 1: Shower seen in a “causal” way from beginning to end

n > 1: Relativistic effects

Time reversal / multiple parts of EAS seen simultaneously

Large “time compression” around part seen at θCher

Effect less important for large r (θCher above shower start)

)2Atmospheric Depth (g/cm100 200 300 400 500 600 700 800 900 1000

Tim

e at

ant

enna

(ns

)

0

2

4

6

8

10

12

14

n=1.0n=1.0003n=n(h)GH (a.u.)

1D shower: r=50m

)2Atmospheric Depth (g/cm100 200 300 400 500 600 700 800 900 1000

Tim

e at

ant

enna

(ns

)

0

20

40

60

80

100

120

140

160

180 n=1.0n=1.0003n=n(h)GH (a.u.)

1D shower: r=400m


Time compression at detector (apparent time)

“Compression factor” fc ∝ |1− n cos θi| ⇒ ~A ∝ NRfc

Maximum compression in time when θi → θCher = cos−1(

1n

)

h → hstart and fc → 0

hstart increases with r and decreases with n

h (m)0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

(ns

/m)

cf

-510

-410

-310

-210

-110

1

num

ber

of p

artic

les

0

10

20

30

40

50

60

70

610×

r=50m

r=100m

r=150m

r=400m

GH

r(m)

θCher

θCher

θCher

50 100 150

h(km)

6

4

2


signal of vertical vs non-vertical showers

Non-vertical showers away from the core (large r)

θi closer to θCher at lower altitudes

Higher compression closer to shower maximum

Higher signal than vertical showers away from the core

In agreement with analytical treatment(Gousset, Ravel and Roy, Astropar Phys 22, 103, 2004)

h (m)0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

| iθ|1

-n c

os

-610

-510

-410

-310

-210

-110

num

ber

of p

artic

les

0

10

20

30

40

50

60

70

80610×

°=50θ| - i

θ|1-n cos

°=0θ| - i

θ|1-n cos

°=50θ GH -

°=0θ GH -

fc ∝ |1− n cos θi|

~A ∝ NRfc

Compression factor vs height of emission


Full ZHAireS sim: Effect of refractive index

Bipolar pulses

Influence of n on pulse: Interplay between nand geometrical parameters (r, R, N , etc..)

time (ns)1400 1500 1600 1700 1800 1900 2000 2100

(V

/m)

EW

E

-2

0

2

4

6

8

-610×

Start time of pulse: later start as n increasesPulse height and width: Net effect depends on r

Influence of n decreases with distance r to core

time (ns)0 5 10 15 20

(V

/m)

EW

E

0

0.2

0.4

0.6

0.8

-310× (h)effn=nn=1.0000n=1.0003

time (ns)0 20 40 60 80 100 120 140 160

(V

/m)

EW

E

-2

0

2

4

6

8

10

12

14

-610× (h)effn=nn=1.0000n=1.0003

r = 100m E of core r = 400m E of core


Signal at 60MHz: Asymmetries

N

S

W E

BB

θ≠0 leads to φ dependance

geo-magnetic

θ=0

geo-magnetic

geo-magnetic

Askar‘yanAskar‘yan Askar‘yan


Asymmetries: dependance on φ


Some examples of prototype showers

Time (ns)-350 -300 -250 -200 -150 -100 -50 0

(V

/m)

EW

E

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-310×

200m E100m E

50m E25m E

10m E

from SE)°Shower 4 ( zenith 50

Time (ns)-872 -870 -868 -866 -864 -862 -860 -858 -856 -854 -852

E (

V/m

)

-0.1

-0.05

0

0.05

0.1

0.15

-310× from SE)°Shower 5 ( zenith 70

EWE

NSE

VertE

Antenna 400m E of core


Questions?


Monte Carlo simulation of radio pulses in atmospheric

Documents

Transcript of Monte Carlo simulation of radio pulses in atmospheric