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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
>
>
--
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.edu
Received on Wed Aug 14 2013 - 22:53:15 CEST