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From: Alberto Fasso' <fasso_at_slac.stanford.edu>

Date: Wed, 14 Aug 2013 04:44:16 -0700 (PDT)

<alpine.LRH.2.00.1308070051440.17472_at_yakut15.slac.stanford.edu> <000501ce98cd$a6cfb1b0$f46f1510$_at_ift.uib.no>

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

Dear Kristian,

yes, when plotting dPhi/d(log E), the linear y-axis is to be preferred because

then the areas under the curve are proportional to the corresponding integrals.

But still, the general shape of the spectrum is conserved: for instance you

see peaks where there are peaks, and a constant spectrum where the spectrum

goes as 1/E. In other words, you lose the quantitative information, but you

keep the qualitative one (the "feeling in which energy region you have

more/less neutrons" mentioned by Vasilis). On the contrary, plotting dPhi/dE,

either whith y linear or logarithmic, makes you lose all useful information.

Unfortunately, this type of plot is often found even in textbooks.

Alberto

On Wed, 14 Aug 2013, Kristian Ytre-Hauge wrote:

*> 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
*

*>
*

*>
*

Date: Wed, 14 Aug 2013 04:44:16 -0700 (PDT)

<alpine.LRH.2.00.1308070051440.17472_at_yakut15.slac.stanford.edu> <000501ce98cd$a6cfb1b0$f46f1510$_at_ift.uib.no>

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

Dear Kristian,

yes, when plotting dPhi/d(log E), the linear y-axis is to be preferred because

then the areas under the curve are proportional to the corresponding integrals.

But still, the general shape of the spectrum is conserved: for instance you

see peaks where there are peaks, and a constant spectrum where the spectrum

goes as 1/E. In other words, you lose the quantitative information, but you

keep the qualitative one (the "feeling in which energy region you have

more/less neutrons" mentioned by Vasilis). On the contrary, plotting dPhi/dE,

either whith y linear or logarithmic, makes you lose all useful information.

Unfortunately, this type of plot is often found even in textbooks.

Alberto

On Wed, 14 Aug 2013, Kristian Ytre-Hauge wrote:

-- Alberto Fasso` SLAC-RP, MS 48, 2575 Sand Hill Road, Menlo Park CA 94025 Phone: (1 650) 926 4762 Fax: (1 650) 926 3569 fasso_at_slac.stanford.eduReceived on Wed Aug 14 2013 - 22:53:15 CEST

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