... | ... | @@ -501,9 +501,9 @@ are given by (See also Figure [flattop]): |
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[latexmath]
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++++
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\begin{aligned}
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\texttt{TRISE} = t_{R} &= \left(\sqrt{2 \ln(10)} - \sqrt{2 \ln \left(\frac{10}{9} \right)} \right) \sigma_{R}\\
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\mathrm{TRISE} = t_{R} &= \left(\sqrt{2 \ln(10)} - \sqrt{2 \ln \left(\frac{10}{9} \right)} \right) \sigma_{R}\\
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& = 1.6869 \sigma_{R} \\
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\texttt{TFALL} = t_{F} &= \left(\sqrt{2 \ln(10)} - \sqrt{2 \ln \left(\frac{10}{9} \right)} \right) \sigma_{F}\\
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\mathrm{TFALL} = t_{F} &= \left(\sqrt{2 \ln(10)} - \sqrt{2 \ln \left(\frac{10}{9} \right)} \right) \sigma_{F}\\
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& = 1.6869 \sigma_{F}\end{aligned}
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++++
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... | ... | @@ -513,7 +513,7 @@ the profile, `TPULSEFWHM`, is defined as (See also Figure [flattop]): |
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[latexmath]
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++++
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\texttt{TPULSEFWHM} = \mathrm{FWHM}_{P} = t_\mathrm{flattop} + \sqrt{2 \ln 2} \left( \sigma_{R} + \sigma_{F} \right)
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\mathrm{TPULSEFWHM} = \mathrm{FWHM}_{P} = t_\mathrm{flattop} + \sqrt{2 \ln 2} \left( \sigma_{R} + \sigma_{F} \right)
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++++
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Total emission time, latexmath:[t_{E}], of this distribution, is a
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... | ... | @@ -523,9 +523,9 @@ see Table [distattrgauss], and is given by: |
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[latexmath]
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++++
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\begin{aligned}
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t_{E}(\texttt{CUTOFFLONG}) &= \mathrm{FWHM}_{P} - \frac{1}{2} (\mathrm{FWHM}_{R} + \mathrm{FWHM}_{F})
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+ \texttt{CUTOFFLONG} (\sigma_{R} + \sigma_{F}) \\
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&= \mathrm{FWHM}_{P} + \frac{\texttt{CUTOFFLONG} - \sqrt{2 \ln 2}}{1.6869} (\texttt{TRISE} + \texttt{TFALL})\end{aligned}
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t_{E}(\mathrm{CUTOFFLONG}) &= \mathrm{FWHM}_{P} - \frac{1}{2} (\mathrm{FWHM}_{R} + \mathrm{FWHM}_{F})
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+ \mathrm{CUTOFFLONG} (\sigma_{R} + \sigma_{F}) \\
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&= \mathrm{FWHM}_{P} + \frac{\mathrm{CUTOFFLONG} - \sqrt{2 \ln 2}}{1.6869} (\mathrm{TRISE} + \mathrm{TFALL})\end{aligned}
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++++
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Finally, we can also impose oscillations over the flat-top portion of
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... | ... | @@ -536,7 +536,7 @@ oscillation periods will be present during the |
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latexmath:[t_\mathrm{flattop}] portion of the pulse. `FTOSCAMPLITUDE`
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defines the amplitude of those oscillations in percentage of the average
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profile amplitude during latexmath:[t_\mathrm{flattop}]. So, for
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example, if we set latexmath:[\texttt{FTOSCAMPLITUDE} = 5], and the
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example, if we set latexmath:[\mathrm{FTOSCAMPLITUDE} = 5], and the
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amplitude of the profile is equal to latexmath:[1.0] during
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latexmath:[t_\mathrm{flattop}], the amplitude of the oscillation will
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be latexmath:[0.05].
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... | ... | @@ -896,7 +896,7 @@ emitted particle’s momentum in a random way: |
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[latexmath]
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++++
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\begin{aligned}
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p_{total} &= \sqrt{\left(\frac{\texttt{EKIN}}{mc^{2}} + 1\right)^{2} - 1} \\
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p_{total} &= \sqrt{\left(\frac{\mathrm{EKIN}}{mc^{2}} + 1\right)^{2} - 1} \\
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p_{x} &= p_{total} \sin(\phi) \cos(\theta)) \\
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p_{y} &= p_{total} \sin(\phi) \sin(\theta)) \\
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p_{z} &= p_{total} |{\cos(\theta)}|
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... | ... | |