Difference between revisions of "HRRL Simulations"

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[http://wiki.iac.isu.edu/index.php/HRRL Go Back]
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Dose Goal:  25 mRem/year to public (after ceiling assuming occupied 1/16 of the time)  and 2 mrem/hr.
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Mark Balzer: 282-5652
 
Mark Balzer: 282-5652
  
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Low energy gamma cutoff = 60 keV
 
Low energy gamma cutoff = 60 keV
  
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=Minimum HERRL Running Condition=
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= HRRL Running Conditions=
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==8 mA ==
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A 2" x 4" x 8 " Al brick was used as a FC by placing it at the exit port of the HRRL after a 90 degree magnet bends electrons towards the HRRL experimental Cell.  The output of a FC after the 90 degree bend at a beam energy of 3 MeV, I= 8 mA, pulse width = 25 ns, and rep rate of 60 Hz is shown in the scope picture below. 
  
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The output of a FC after the 90 degrees bend at a beam energy of 3 MeV, I= 8 mA, pulse width = 32 ns, and rep rate of 60 Hz.
 
 
[[Image:HRRL_3MeV_FC_output_10_10_08.png|200px]]
 
[[Image:HRRL_3MeV_FC_output_10_10_08.png|200px]]
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An accelerator operator will be able to tune the beam at this setting.
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=Copper Simulation=
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A 10 m x 10m x 10m HURL experimental cells was simulated in which a 2 mm Copper target representing detectors was installed 1 m from the beam upstream wall and centered in the remaining dimensions of the room.  The ceiling was set 3m above the copper target.
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== 3 MeV ==
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A comparison between MCNP-X and GEANT4:  Both simulations threw <math>10^6</math> electrons onto a 2 mm thick Copper target located in the HRRL experimental Cell.
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{| border="1"  |cellpadding="20" cellspacing="0
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|-
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|  Simulation || Gamma Energy deposited per <math>10^6</math> incident <math>e^-</math>
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|-
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|  || Inside Cell || above 6" thick concrete Cell ceiling || Ion Chamber in HRRL Cell || Peak current limit at 25 ns and 1kHz
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|-
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|MCNPX || <math>2.53 \times 10^4</math> MeV (rad/C)|| <math>1.3 \times 10^3</math> MeV (rad/C) || <math>9.5 \times 10^{-18} rem/e</math> || <math>7.9</math> mA
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|-
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|GEANT4||<math>3.1 \times 10^4</math> MeV (rad/C)|| <math>5.6 \times 10^3</math> MeV (rad/C)
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|}
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Converting the energy from MeV to Joules
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 +
:<math>1 \times 10^4 MeV \times \frac{1.6 \times 10^{-19} J }{10^{-6} MeV} =  1.6 \times 10^{-9} J</math>
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In terms of the energy per  beam current charge we would have
 +
 +
:<math>\frac{ 1.6 \times 10^{-9} J}{10^6 e^-} \times \frac{1 e^-}{1.6 \times 10^{-19} C} = \frac { 10 krad}{C}</math>
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(I assume a 100 kg person ( 1 rad = 1 J/100 kg) Units are not consistent. There is a mass unit missing in this conversion. Vakho)
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Average Current for a 2mrad/hr dose limit
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:<math>\frac{ 2 \times 10^{-3} rad}{3600 sec} \times \frac{1 C }{10^{4} rad} = 5.6 \times 10^{-11} Coul/sec = 56 pA = 0.05 nA</math>
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How can you get 56 pA from the HRRL?
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Currently you can see an 8 mA current on a FC with a 25 nSecond pulse width.
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: <math>\Rightarrow 8 \times 10^{-3} Couls/sec \times 25 \times 10^{-9} seconds = 2 \times 10^{-10} Coul</math>
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Therefore: Restricting to HRRL to 2 mA peak currents with 25 nSec pulse widths and 1 Hz should keep the dose beyond a 6" concrete ceiling below 2 mrad/hr.  2 mA peak HRRL currents have been [http://www.iac.isu.edu/mediawiki/index.php/5-19-08#FC_performance measured before] using a FC from JLab.
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; What running conditions will result in less than 25 mrad of dose for 2000 hours (1 year) of operation
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:<math>\frac{ 25 \times 10^{-3} rad}{2000 hours} \times \frac{ 1 hr}{3600 sec} \frac{1 C }{10^{4} rad} = 3.47 \times 10^{-13} Coul/sec</math>
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: <math>\Rightarrow I_{HRRL}^{peak} = 0.008</math> mA
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[[Image:E_Gammas_3MeV_e-_Cu_MCNPX.jpg | 400 px]]
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[[Image:E_Gammas_3MeV_e-_Cu_GEANT4.gif | 400 px]]
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[[Image:E_Gammas_Above6incCeiling_3MeV_e-_Cu_MCNPX.jpg | 400 px]]
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[[Image:E_Gammas_Above6incCeiling_3MeV_e-_Cu_GEANT4.gif | 400 px]]
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The above predictions only considered gammas with energies above 100 keV.  With the 100 keV cut removed I still see less than <math>10^4</math> MeV (6770 MeV) of deposited energy per <math> 10^6</math> incident 3 MeV electrons.
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[[Image:E_Gammas_Above6incCeilingNoCut_3MeV_e-_Cu_GEANT4.gif | 400 px]]
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== 7 MeV ==
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{| border="1"  |cellpadding="20" cellspacing="0
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|-
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|Simulation || Gamma Energy deposited per <math>10^6</math> incident <math>e^-</math>
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|-
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|  || Inside Cell || above 6" thick concrete Cell ceiling || Ion Chamber in HRRL Cell || Peak current limit at 25 ns and 1 kHz
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|-
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|MCNPX || <math>1.41 \times 10^5</math> MeV (rad/C)|| <math>1.38 \times 10^4</math> MeV || <math>6.2 \times 10^{-17} rem/e</math> || <math>0.6</math> mA
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|-
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|GEANT4||<math> 1.01 \times 10^5</math> MeV (rad/C)||
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|}
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[[Image:GammaProfile_10-14-08.gif | 200 px]]
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The GEANT4 histograms below are from 100 k Events not 1 Million like Vakhos.
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[[Image:Gammas_7MeV_e-_Cu_100kEvents_10-14-08.gif | 200 px]]
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[[Image:Gammas_.g.t.100keV_7MeV_e-_Cu_100kEvents_10-14-08.gif | 200 px]]
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[[Image:E_Gammas_7MeV_e-_Cu_MCNPX.jpg | 400 px | 200 px]]
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[[Image:E_Gammas_Above_Concrete_7MeV_e-_Cu_MCNPX.jpg | 400 px | 200 px]]
  
 
=Tungsten SImulation=
 
=Tungsten SImulation=
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|15.0 || 13.3E-6
 
|15.0 || 13.3E-6
 
|}
 
|}
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== Concrete Definition and Stopping Power ==
 
== Concrete Definition and Stopping Power ==
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[http://www.iac.isu.edu/mediawiki/index.php/HRRL Go back]
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[http://wiki.iac.isu.edu/index.php/HRRL Go Back]

Latest revision as of 06:34, 5 February 2009

Go Back


Dose Goal: 25 mRem/year to public (after ceiling assuming occupied 1/16 of the time) and 2 mrem/hr.

Mark Balzer: 282-5652

Brian Oborn: 282- 6243

This document describes the simulations performed to estimate the radiological background in the event that a 1 nA electron current from the HRRL enters the experimental cell.

Radiation monitors: Ludlum Model 45-8.

Low energy gamma cutoff = 60 keV

HRRL Running Conditions

8 mA

A 2" x 4" x 8 " Al brick was used as a FC by placing it at the exit port of the HRRL after a 90 degree magnet bends electrons towards the HRRL experimental Cell. The output of a FC after the 90 degree bend at a beam energy of 3 MeV, I= 8 mA, pulse width = 25 ns, and rep rate of 60 Hz is shown in the scope picture below.

HRRL 3MeV FC output 10 10 08.png

An accelerator operator will be able to tune the beam at this setting.

Copper Simulation

A 10 m x 10m x 10m HURL experimental cells was simulated in which a 2 mm Copper target representing detectors was installed 1 m from the beam upstream wall and centered in the remaining dimensions of the room. The ceiling was set 3m above the copper target.

3 MeV

A comparison between MCNP-X and GEANT4: Both simulations threw [math]10^6[/math] electrons onto a 2 mm thick Copper target located in the HRRL experimental Cell.

Simulation Gamma Energy deposited per [math]10^6[/math] incident [math]e^-[/math]
Inside Cell above 6" thick concrete Cell ceiling Ion Chamber in HRRL Cell Peak current limit at 25 ns and 1kHz
MCNPX [math]2.53 \times 10^4[/math] MeV (rad/C) [math]1.3 \times 10^3[/math] MeV (rad/C) [math]9.5 \times 10^{-18} rem/e[/math] [math]7.9[/math] mA
GEANT4 [math]3.1 \times 10^4[/math] MeV (rad/C) [math]5.6 \times 10^3[/math] MeV (rad/C)

Converting the energy from MeV to Joules

[math]1 \times 10^4 MeV \times \frac{1.6 \times 10^{-19} J }{10^{-6} MeV} = 1.6 \times 10^{-9} J[/math]

In terms of the energy per beam current charge we would have

[math]\frac{ 1.6 \times 10^{-9} J}{10^6 e^-} \times \frac{1 e^-}{1.6 \times 10^{-19} C} = \frac { 10 krad}{C}[/math]
(I assume a 100 kg person ( 1 rad = 1 J/100 kg) Units are not consistent. There is a mass unit missing in this conversion. Vakho)

Average Current for a 2mrad/hr dose limit

[math]\frac{ 2 \times 10^{-3} rad}{3600 sec} \times \frac{1 C }{10^{4} rad} = 5.6 \times 10^{-11} Coul/sec = 56 pA = 0.05 nA[/math]

How can you get 56 pA from the HRRL?

Currently you can see an 8 mA current on a FC with a 25 nSecond pulse width.

[math]\Rightarrow 8 \times 10^{-3} Couls/sec \times 25 \times 10^{-9} seconds = 2 \times 10^{-10} Coul[/math]

Therefore: Restricting to HRRL to 2 mA peak currents with 25 nSec pulse widths and 1 Hz should keep the dose beyond a 6" concrete ceiling below 2 mrad/hr. 2 mA peak HRRL currents have been measured before using a FC from JLab.


What running conditions will result in less than 25 mrad of dose for 2000 hours (1 year) of operation
[math]\frac{ 25 \times 10^{-3} rad}{2000 hours} \times \frac{ 1 hr}{3600 sec} \frac{1 C }{10^{4} rad} = 3.47 \times 10^{-13} Coul/sec[/math]
[math]\Rightarrow I_{HRRL}^{peak} = 0.008[/math] mA

E Gammas 3MeV e- Cu MCNPX.jpg E Gammas 3MeV e- Cu GEANT4.gif

E Gammas Above6incCeiling 3MeV e- Cu MCNPX.jpg E Gammas Above6incCeiling 3MeV e- Cu GEANT4.gif


The above predictions only considered gammas with energies above 100 keV. With the 100 keV cut removed I still see less than [math]10^4[/math] MeV (6770 MeV) of deposited energy per [math] 10^6[/math] incident 3 MeV electrons.

E Gammas Above6incCeilingNoCut 3MeV e- Cu GEANT4.gif

7 MeV

Simulation Gamma Energy deposited per [math]10^6[/math] incident [math]e^-[/math]
Inside Cell above 6" thick concrete Cell ceiling Ion Chamber in HRRL Cell Peak current limit at 25 ns and 1 kHz
MCNPX [math]1.41 \times 10^5[/math] MeV (rad/C) [math]1.38 \times 10^4[/math] MeV [math]6.2 \times 10^{-17} rem/e[/math] [math]0.6[/math] mA
GEANT4 [math] 1.01 \times 10^5[/math] MeV (rad/C)

GammaProfile 10-14-08.gif

The GEANT4 histograms below are from 100 k Events not 1 Million like Vakhos.


Gammas 7MeV e- Cu 100kEvents 10-14-08.gif

Gammas .g.t.100keV 7MeV e- Cu 100kEvents 10-14-08.gif

E Gammas 7MeV e- Cu MCNPX.jpg

E Gammas Above Concrete 7MeV e- Cu MCNPX.jpg

Tungsten SImulation

I created a world volume filled with Air to represent the experimental cell.

I created a 2mm thick tungsten target that is 30 cm x 30 cm in area.

The image below shows several electrons hitting the tungsten foil, then scattering in air. The red lines are electrons and the green ones are photons.


HRRL ExperimentCell World 1.jpg

Run 1

I then ran 1 million events in which an incident 7 MeV electron hit the 2 mm thick Tungsten with the physics processes 

    if (particleName == "gamma") {
     // gamma         
   pmanager->AddDiscreteProcess(new G4PhotoElectricEffect);
     pmanager->AddDiscreteProcess(new G4ComptonScattering);
     pmanager->AddDiscreteProcess(new G4GammaConversion);
     
   } else if (particleName == "e-") {
     //electron
     pmanager->AddProcess(new G4MultipleScattering,-1, 1,1);
     pmanager->AddProcess(new G4eIonisation,       -1, 2,2);
     pmanager->AddProcess(new G4eBremsstrahlung,   -1, 3,3);

I only kept gamma which had a momentum component towards the ceiling (p_y>0).

The energy distribution (in MeV) of the gammas headed towards the ceiling is shown below. Of the 1 million electrons incident on the 2 mm thick Tungsten target, only 70,000 gammas were headed towards the cieling. This does not mean that they hit it, they could have hit the wall.

Run 1 Gamma E dist.gif

If I sum the above distribution I see a total energy of 43,987 MeV going up from the 1 million 7 MeV electrons hitting the 2mm Tungsten target.

1 Rad =[math]\frac{J}{100 kg}[/math] = the amount of energy absorbed per 100 kg of material

To calculate the worst possible case lets assume all of the radiation is absorbed by a person (there is no concrete ceiling).

Converting the energy from MeV to Joules

[math]4.4 \times 10^4 MeV \times \frac{1.6 \times 10^{-19} J }{10^{-6} MeV} = 4.4 \times 10^{-9} J[/math]

In terms of the energy per beam current charge we would have

[math]\frac{4.4 \times 10^{-9} J}{10^6 e^-} \times \frac{1 e^-}{1.6 \times 10^{-19} C} = \frac {44 krad}{C}[/math]


I we ran the HRRL for 1 hour at the maximum beam current of 80 mA per 100 ns pulse and 1 kHz rep rate then the dose to the ceiling would be

[math]80 mA \times 100 ns = 8 \times 10^{-9} Coul \times \frac{1000 pulses}{sec} \times \frac{3600 sec}{hr} = 0.0288 Coul/hr \times \frac {44 krad}{C} = 1.4 kRad/hr[/math]

The total photon radiation hitting the upper half of the experimental cell is predicted to be 1.4 krad/hr. To determine the dose on a radiation detector you just need to scale by the solid angle.

Mark Balzer tells me that the ion chambers are cylinders of length 4 inches and 1 inch in diameter. The ion chamber's cylindrical axis is mounted parallel to the ceiling. We will be limited to running with beam current that generate 2 mRad/hr or less in a single ion chamber. As a first estimate I will treat the cylinder as having a rectangular surface area of 4 " x 1 " = 4 in^2 = 25.8 cm^2. The ion chamber is on the ceiling which is about 6 meters from the beam pipe. The solid angle is thus

[math]\frac{A}{r^2} = \frac{25.8}{600^2} = 7.2 \times 10^-5 strad[/math].

The predicted rate in an ion chamber would then be

[math]1.4 kRad/hr \times \frac{7.2 \times 10^-5}{2 \pi} = 16 mRad/hr [/math]
[math]\Rightarrow[/math] our max beam current for 1 mRad/hr would be [math]\frac{80}{16}[/math] = 5 mA peak

Or in terms of an average current

[math]5 mA \times 0.1 \mu s * 1000/sec = 0.5 \mu A[/math] average

Run 2: Ceiling Penetration

Setup

The picture below shows the simulation World volume. A red electron beam enters the HRRL experimental cell from the left side and hits a 2 mm thick Tungsten target shown as the white vertical line inside the white inner box. The yellow box is a detector tracking cell. The roof is shown as 2 horizontal lines near the top of the World volume.

Run2 HRRL ExptCell Ceiling.jpg


A few interesting events:

ElectronCreatesGammaOnHRRLExptCellCeiling.jpg GammaBouncesintoCeilinginHRRLExptCell.jpg

Figure GAT: Location of Gamma absoption in the HRRL experimental Cell


Figure GAT shows the location of gamma absorption in the HRRL. There are 5 clear locations which see a lot of gammas. The two circular black disks located near the center of the experimental cell represent the windows of a virtual detector box used in the simulation. . The Tungsten foil appears in between these two circular disks. The two remaining locations which see a high gamma flux are on the walls of the HRRL experimental cell in the forward direction. The majority of the gammas directed to the ceiling appear to be absorbed at that location. The goal of this simulation is to estimate the radiation dose inside the HRRL experimental cell at the ceiling. I will divide the ceiling into square pixels having an area of 1 foot square in order to approximate a human standing on the ceiling at that location. I will then choose the pixel with the highest photon flux to estimate a dose. This pixel will most likely be directly above the beamline and near the end of the beam line in the cell.


Ceiling Photon distribution

Photon Energy -to- Dose

DoseCalcFromEgamma.jpg

Photon Energy Dose Conversion Coeff
(MeV) rem [math]cm^2[/math] s/ hr
0.01 3.96E-6
0.03 0.582E-6
0.05 0.290E-6
0.07 0.258E-6
0.1 0.283E-6
0.15 0.379E-6
0.2 0.501E-6
0.25 0.631E-6
0.3 0.759E-6
0.35 0.878E-6
0.4 0.985E-6
0.45 1.08E-6
0.5 1.17E-6
0.55 1.27E-6
0.6 1.36E-6
0.65 1.44E-6
0.7 1.52E-6
0.8 1.68E-6
1.0 1.98E-6
1.4 2.51E-6
1.8 2.99E-6
2.2 3.42E-6
2.6 3.82E-6
2.8 4.01E-6
3.25 4.41E-6
3.75 4.83E-6
4.25 5.23E-6
4.75 5.60E-6
5.0 5.80E-6
5.25 6.01E-6
5.75 6.37E-6
6.25 6.74E-6
6.75 7.11E-6
7.5 7.66E-6
9.0 8.77E-6
11.0 10.3E-6
13.0 11.8E-6
15.0 13.3E-6


Concrete Definition and Stopping Power

A 6 inch concrete floor is assumed to exist on the top of the experimental cell which will block radiation from penetrating to the offices above the cell.

Stopping power from NIST

PortlandConcreteStoppingPower.png

Composition of CONCRETE, PORTLAND: Density (g/cm3) = 2.30000E+00 Mean Excitation Energy (eV) = 135.200000

COMPOSITION:

Atomic Number Fraction by Weight
1 0.010000
6 0.001000
8 0.529107
11 0.016000
12 0.002000
13 0.033872
14 0.337021
19 0.013000
20 0.044000
26 0.014000

(required)

Kinetic Energy(MeV)

Stopping Power (MeV cm2/g) || CSDA Range(g/cm2) || RadiationYield || Density EffectParameter

Collision

Radiative || Total

1.000E-02 1.804E+01 5.754E-03 1.805E+01 3.207E-04 1.710E-04 0.000E+00
1.250E-02 1.526E+01 5.864E-03 1.526E+01 4.720E-04 2.072E-04 0.000E+00
1.500E-02 1.330E+01 5.942E-03 1.330E+01 6.480E-04 2.419E-04 0.000E+00
1.750E-02 1.184E+01 5.999E-03 1.184E+01 8.476E-04 2.755E-04 0.000E+00
2.000E-02 1.070E+01 6.044E-03 1.071E+01 1.070E-03 3.080E-04 0.000E+00
2.500E-02 9.049E+00 6.107E-03 9.056E+00 1.580E-03 3.704E-04 0.000E+00
3.000E-02 7.899E+00 6.153E-03 7.905E+00 2.173E-03 4.298E-04 0.000E+00
3.500E-02 7.049E+00 6.189E-03 7.055E+00 2.844E-03 4.867E-04 0.000E+00
4.000E-02 6.393E+00 6.220E-03 6.400E+00 3.589E-03 5.415E-04 0.000E+00
4.500E-02 5.872E+00 6.249E-03 5.878E+00 4.405E-03 5.944E-04 0.000E+00
5.000E-02 5.446E+00 6.276E-03 5.453E+00 5.289E-03 6.457E-04 0.000E+00
5.500E-02 5.092E+00 6.302E-03 5.099E+00 6.238E-03 6.955E-04 0.000E+00
6.000E-02 4.793E+00 6.328E-03 4.799E+00 7.250E-03 7.440E-04 0.000E+00
7.000E-02 4.315E+00 6.381E-03 4.321E+00 9.450E-03 8.375E-04 0.000E+00
8.000E-02 3.948E+00 6.437E-03 3.955E+00 1.187E-02 9.269E-04 0.000E+00
9.000E-02 3.659E+00 6.497E-03 3.665E+00 1.450E-02 1.013E-03 0.000E+00
1.000E-01 3.425E+00 6.560E-03 3.431E+00 1.732E-02 1.096E-03 0.000E+00
1.250E-01 2.996E+00 6.733E-03 3.003E+00 2.514E-02 1.292E-03 0.000E+00
1.500E-01 2.706E+00 6.925E-03 2.713E+00 3.393E-02 1.477E-03 0.000E+00
1.750E-01 2.498E+00 7.134E-03 2.505E+00 4.353E-02 1.652E-03 0.000E+00
2.000E-01 2.341E+00 7.357E-03 2.349E+00 5.385E-02 1.819E-03 0.000E+00
2.500E-01 2.124E+00 7.843E-03 2.132E+00 7.627E-02 2.137E-03 0.000E+00
3.000E-01 1.982E+00 8.377E-03 1.990E+00 1.006E-01 2.438E-03 0.000E+00
3.500E-01 1.883E+00 8.952E-03 1.892E+00 1.264E-01 2.728E-03 8.781E-04
4.000E-01 1.811E+00 9.563E-03 1.820E+00 1.534E-01 3.011E-03 1.827E-02
4.500E-01 1.756E+00 1.021E-02 1.766E+00 1.813E-01 3.290E-03 3.821E-02
5.000E-01 1.714E+00 1.088E-02 1.725E+00 2.099E-01 3.565E-03 5.986E-02
5.500E-01 1.681E+00 1.159E-02 1.693E+00 2.392E-01 3.839E-03 8.276E-02
6.000E-01 1.655E+00 1.231E-02 1.668E+00 2.690E-01 4.112E-03 1.066E-01
7.000E-01 1.618E+00 1.383E-02 1.632E+00 3.296E-01 4.657E-03 1.562E-01
8.000E-01 1.593E+00 1.543E-02 1.609E+00 3.914E-01 5.204E-03 2.072E-01
9.000E-01 1.577E+00 1.709E-02 1.594E+00 4.539E-01 5.754E-03 2.587E-01
1.000E+00 1.566E+00 1.882E-02 1.585E+00 5.168E-01 6.308E-03 3.102E-01
1.250E+00 1.553E+00 2.339E-02 1.577E+00 6.751E-01 7.716E-03 4.363E-01
1.500E+00 1.551E+00 2.828E-02 1.580E+00 8.335E-01 9.157E-03 5.566E-01
1.750E+00 1.555E+00 3.342E-02 1.588E+00 9.914E-01 1.063E-02 6.704E-01
2.000E+00 1.560E+00 3.876E-02 1.599E+00 1.148E+00 1.213E-02 7.777E-01
2.500E+00 1.575E+00 4.998E-02 1.625E+00 1.459E+00 1.520E-02 9.746E-01
3.000E+00 1.590E+00 6.176E-02 1.651E+00 1.764E+00 1.835E-02 1.152E+00
3.500E+00 1.604E+00 7.400E-02 1.678E+00 2.064E+00 2.155E-02 1.312E+00
4.000E+00 1.617E+00 8.662E-02 1.704E+00 2.360E+00 2.479E-02 1.459E+00
4.500E+00 1.630E+00 9.956E-02 1.729E+00 2.651E+00 2.805E-02 1.595E+00
5.000E+00 1.641E+00 1.128E-01 1.754E+00 2.938E+00 3.134E-02 1.721E+00
5.500E+00 1.651E+00 1.263E-01 1.778E+00 3.221E+00 3.465E-02 1.839E+00
6.000E+00 1.661E+00 1.400E-01 1.801E+00 3.501E+00 3.796E-02 1.949E+00
7.000E+00 1.678E+00 1.680E-01 1.846E+00 4.049E+00 4.459E-02 2.152E+00
8.000E+00 1.693E+00 1.968E-01 1.890E+00 4.584E+00 5.122E-02 2.334E+00
9.000E+00 1.706E+00 2.261E-01 1.932E+00 5.108E+00 5.781E-02 2.500E+00
1.000E+01 1.718E+00 2.558E-01 1.973E+00 5.620E+00 6.437E-02 2.652E+00
1.250E+01 1.742E+00 3.320E-01 2.074E+00 6.855E+00 8.050E-02 2.984E+00
1.500E+01 1.761E+00 4.102E-01 2.171E+00 8.033E+00 9.619E-02 3.267E+00
1.750E+01 1.777E+00 4.899E-01 2.267E+00 9.160E+00 1.114E-01 3.513E+00
2.000E+01 1.791E+00 5.707E-01 2.362E+00 1.024E+01 1.261E-01 3.731E+00
2.500E+01 1.813E+00 7.350E-01 2.548E+00 1.228E+01 1.540E-01 4.106E+00
3.000E+01 1.831E+00 9.020E-01 2.733E+00 1.417E+01 1.799E-01 4.422E+00
3.500E+01 1.845E+00 1.071E+00 2.916E+00 1.594E+01 2.041E-01 4.694E+00
4.000E+01 1.857E+00 1.241E+00 3.099E+00 1.761E+01 2.266E-01 4.934E+00
4.500E+01 1.868E+00 1.413E+00 3.281E+00 1.917E+01 2.476E-01 5.148E+00
5.000E+01 1.877E+00 1.586E+00 3.463E+00 2.066E+01 2.673E-01 5.342E+00
5.500E+01 1.886E+00 1.760E+00 3.646E+00 2.206E+01 2.858E-01 5.519E+00
6.000E+01 1.893E+00 1.934E+00 3.828E+00 2.340E+01 3.032E-01 5.681E+00
7.000E+01 1.906E+00 2.286E+00 4.192E+00 2.590E+01 3.350E-01 5.971E+00
8.000E+01 1.918E+00 2.639E+00 4.557E+00 2.819E+01 3.634E-01 6.225E+00
9.000E+01 1.928E+00 2.994E+00 4.922E+00 3.030E+01 3.891E-01 6.451E+00
1.000E+02 1.936E+00 3.351E+00 5.288E+00 3.226E+01 4.123E-01 6.654E+00
1.250E+02 1.954E+00 4.248E+00 6.203E+00 3.662E+01 4.620E-01 7.087E+00
1.500E+02 1.969E+00 5.151E+00 7.120E+00 4.038E+01 5.025E-01 7.443E+00
1.750E+02 1.981E+00 6.059E+00 8.040E+00 4.368E+01 5.363E-01 7.746E+00
2.000E+02 1.992E+00 6.969E+00 8.961E+00 4.662E+01 5.650E-01 8.010E+00
2.500E+02 2.010E+00 8.797E+00 1.081E+01 5.170E+01 6.114E-01 8.451E+00
3.000E+02 2.024E+00 1.063E+01 1.266E+01 5.597E+01 6.474E-01 8.813E+00
3.500E+02 2.036E+00 1.247E+01 1.451E+01 5.965E+01 6.764E-01 9.119E+00
4.000E+02 2.046E+00 1.432E+01 1.636E+01 6.290E+01 7.003E-01 9.385E+00
4.500E+02 2.055E+00 1.616E+01 1.822E+01 6.579E+01 7.204E-01 9.620E+00
5.000E+02 2.064E+00 1.801E+01 2.008E+01 6.841E+01 7.376E-01 9.830E+00
5.500E+02 2.071E+00 1.986E+01 2.194E+01 7.079E+01 7.525E-01 1.002E+01
6.000E+02 2.078E+00 2.172E+01 2.379E+01 7.298E+01 7.656E-01 1.019E+01
7.000E+02 2.090E+00 2.543E+01 2.752E+01 7.688E+01 7.874E-01 1.050E+01
8.000E+02 2.100E+00 2.914E+01 3.124E+01 8.029E+01 8.051E-01 1.077E+01
9.000E+02 2.109E+00 3.286E+01 3.497E+01 8.331E+01 8.197E-01 1.100E+01
1.000E+03 2.117E+00 3.658E+01 3.870E+01 8.603E+01 8.320E-01 1.121E+01



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