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From: Kristian Ytre-Hauge <kristian.ytre-hauge_at_ift.uib.no>

Date: Wed, 14 Aug 2013 21:52:48 +0200

<alpine.LRH.2.00.1308070051440.17472_at_yakut15.slac.stanford.edu>

In-Reply-To: <alpine.LRH.2.00.1308070051440.17472_at_yakut15.slac.stanford.edu>

Subject: RE: plotting of neutron fluence in flair

Date: Wed, 14 Aug 2013 11:07:07 +0200

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Dear Alberto and Vasilis,

Thank you both for very clarifying answers.

I agree with the conclusion that the area of the plotted bins will be

proportional to the corresponding fluence.

In many cases we wish to compare several spectra and wish to use a

logarithmic y-axis in order to make details in all spectra more visible

(e.g. in the flair tutorial).

Am I right to say that we then partially lose the readability we obtain with

a linear y-axis, and therefore should stick to a linear y-axis if possible?

Best regards,

Kristian

-----Original Message-----

From: owner-fluka-discuss_at_mi.infn.it [mailto:owner-fluka-discuss_at_mi.infn.it]

On Behalf Of Alberto Fasso'

Sent: 7. august 2013 10:58

To: fluka-discuss_at_fluka.org

Cc: Vasilis Vlachoudis; Kristian Ytre-Hauge

Subject: RE: plotting of neutron fluence in flair

Hi Kristian,

Vasilis has given you the classical "physical" explanation that is found in

all neutronics textbooks: the name "isolethargic spectrum" comes indeed from

the concept of a neutron spectrum as it is created in a perfect moderator.

And, as Vasilis says, in a perfect moderator the logarithmic neutron energy

loss d(log E) = dE/E is constant with energy, therefore the expression

"isolethargic spectrum" literally means dPhi(E)/d(log E) = const., i.e. a

"flat"

spectrum.

However, the term is generally extended to mean "a spectrum plotted as

dPhi(E)/d(log E) vs. log E", even if such spectrum is far from being flat.

And I must add that this type of plot can be used (better: "must" be used)

not only for neutrons, but for any other type of particle having a spectrum

extended over many orders of magnitude: e.g. photons, muons, or cosmic rays.

Why did I say "must" be used? Because the reason is mathematical, not

physical.

If you want to plot any distribution F(x) of a variable x (not necessarily a

particle spectrum, but ANY distribution) as a function of x, you obviously

plot dF(x)/dx vs x. But if you want to plot it as a function of log x, then

you must plot dF(x)/d(log x)=xdF(x) vs log x. It is a common change of

variable for calculating integrals, as it is taught in elementary calculus.

Using this type of plot, the area subtended by the curve between any pair of

abscissas log(x1) and log(x2) is proportional to the integral of the

distribution between x1 and x2.

This is what Vasilis means by "the isolethargic neutron spectrum gives you

immediately a feeling in which energy region you have more/less neutrons":

you get that feeling because each area of the plotted spectrum is

proportional to the corresponding integral flux.

Alberto

On Tue, 6 Aug 2013, Vasilis Vlachoudis wrote:

*> Hi Kristian,
*

*>
*

*> Please give a look on the neutron lecture of any of our beginers courses.
*

*> https://www.fluka.org/free_download/course/nea2013/Lectures/10_Low_Ene
*

*> rgy_N
*

*> eutrons.pdf
*

*>
*

*> <Xgeo> = geometric mean of the X axis = e^((logEi + lowE[i+1])/2) =
*

*> sqrt(Ei
*

*> * E[i+1])
*

*> Isolethargic units, comes out from the concept of the neutron lethargy
*

*> xi ~=
*

*> 2 / (A + 2/3)
*

*> which is the average logarithmic energy loss of a neutron for each
*

*> collision with a target nucleus A.
*

*>
*

*> As you can see xi is constant therefore you expect that the neutrons
*

*> on average lose the same amount of energy on any collision, therefore
*

*> if you plot the differential of neutron flux per logarithmic energy
*

*> (assuming that the capture is negligible) you should get a flat
*

*> spectrum in the range from 1eV to few
*

*> 100 keV.
*

*> therefore dn/dlnE = Const <=> E*dn/dE = Const <=> E*Flux = Const
*

*>
*

*> In brief, since the neutron moderation is logarithmic, the
*

*> isolethargic neutron spectrum gives you immediately a feeling in which
*

*> energy region you have more/less neutrons
*

*>
*

*> Best Regards
*

*> Vasilis
*

*>
*

*> ______________________________________________________________________
*

*> ______
*

*> From: owner-fluka-discuss_at_mi.infn.it [owner-fluka-discuss_at_mi.infn.it]
*

*> on behalf of Kristian Ytre-Hauge [kristian.ytre-hauge_at_ift.uib.no]
*

*> Sent: 05 August 2013 13:15
*

*> To: fluka-discuss_at_fluka.org
*

*> Subject: plotting of neutron fluence in flair
*

*>
*

*> Dear Fluka experts,
*

*>
*

*> When scoring neutrons with USRTRACK I believe the output in the
*

*> tab.lis file is given in the units
*

*>
*

*> [neut. cm-2 GeV-1 primary-1]
*

*>
*

*> Plotting neutron fluence in flair has previously been discussed here
*

*> and from the discussion I found these statements:
*

*>
*

*> To plot normal fluence like a histogram choose:
*

*>
*

*> X:Low [xl]
*

*>
*

*> Y:Y (with steps)
*

*>
*

*> To plot isolethargic fluence as histogram (logarithmic x-axis):
*

*>
*

*> X = Low [xl]
*

*>
*

*> Y = Y*<Xgeo> (with steps)
*

*>
*

*> My questions are:
*

*>
*

*> 1) What are the advantages of an isolethargic plot, and when should it
*

*> be used?
*

*>
*

*> 2) What are the proper units on the Y-axis for such a plot? In the
*

*> flair tutorial (<quick start guide>) The fluence is given as:
*

*> (dn/dlnE). If someone could explain how we arrive at these units it
*

*> would be much appreciated.
*

*>
*

*>
*

*>
*

*> Best regards,
*

*>
*

*> Kristian Ytre-Hauge
*

Received on Wed Aug 14 2013 - 22:53:14 CEST

Date: Wed, 14 Aug 2013 21:52:48 +0200

<alpine.LRH.2.00.1308070051440.17472_at_yakut15.slac.stanford.edu>

In-Reply-To: <alpine.LRH.2.00.1308070051440.17472_at_yakut15.slac.stanford.edu>

Subject: RE: plotting of neutron fluence in flair

Date: Wed, 14 Aug 2013 11:07:07 +0200

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Sender: owner-fluka-discuss_at_smtp2.mi.infn.it

Dear Alberto and Vasilis,

Thank you both for very clarifying answers.

I agree with the conclusion that the area of the plotted bins will be

proportional to the corresponding fluence.

In many cases we wish to compare several spectra and wish to use a

logarithmic y-axis in order to make details in all spectra more visible

(e.g. in the flair tutorial).

Am I right to say that we then partially lose the readability we obtain with

a linear y-axis, and therefore should stick to a linear y-axis if possible?

Best regards,

Kristian

-----Original Message-----

From: owner-fluka-discuss_at_mi.infn.it [mailto:owner-fluka-discuss_at_mi.infn.it]

On Behalf Of Alberto Fasso'

Sent: 7. august 2013 10:58

To: fluka-discuss_at_fluka.org

Cc: Vasilis Vlachoudis; Kristian Ytre-Hauge

Subject: RE: plotting of neutron fluence in flair

Hi Kristian,

Vasilis has given you the classical "physical" explanation that is found in

all neutronics textbooks: the name "isolethargic spectrum" comes indeed from

the concept of a neutron spectrum as it is created in a perfect moderator.

And, as Vasilis says, in a perfect moderator the logarithmic neutron energy

loss d(log E) = dE/E is constant with energy, therefore the expression

"isolethargic spectrum" literally means dPhi(E)/d(log E) = const., i.e. a

"flat"

spectrum.

However, the term is generally extended to mean "a spectrum plotted as

dPhi(E)/d(log E) vs. log E", even if such spectrum is far from being flat.

And I must add that this type of plot can be used (better: "must" be used)

not only for neutrons, but for any other type of particle having a spectrum

extended over many orders of magnitude: e.g. photons, muons, or cosmic rays.

Why did I say "must" be used? Because the reason is mathematical, not

physical.

If you want to plot any distribution F(x) of a variable x (not necessarily a

particle spectrum, but ANY distribution) as a function of x, you obviously

plot dF(x)/dx vs x. But if you want to plot it as a function of log x, then

you must plot dF(x)/d(log x)=xdF(x) vs log x. It is a common change of

variable for calculating integrals, as it is taught in elementary calculus.

Using this type of plot, the area subtended by the curve between any pair of

abscissas log(x1) and log(x2) is proportional to the integral of the

distribution between x1 and x2.

This is what Vasilis means by "the isolethargic neutron spectrum gives you

immediately a feeling in which energy region you have more/less neutrons":

you get that feeling because each area of the plotted spectrum is

proportional to the corresponding integral flux.

Alberto

On Tue, 6 Aug 2013, Vasilis Vlachoudis wrote:

Received on Wed Aug 14 2013 - 22:53:14 CEST

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