CMS Prediction

A prediction of single event upsets for the CMS tracker includes several assumptions and thus implies a large error bar. First of all, the flux or integrated fluence as a function of radius and rapidity is not exactly known. Moreover, the particles expected in CMS are not mono-energetic, and of various types. Simulations [7] predict that the particle zoo is dominated by charged hadrons, especially pions, with a momentum below $1\,\rm GeV/c$. Regarding the nuclear interaction cross-section resonance peak of $300\,\rm MeV/c$ pions on protons [3], a straight SEU extrapolation is likely to result in an overestimation.

The heavy ion results suggest a cross-section of approximately $10^{-12}\,\rm cm^2$ for the CMS environment, which is in fact half the value measured with pions. Thus, the direct extrapolation of the pion results can be considered as a worst case scenario.

The average flux in the CMS tracker has been derived from a simulated radiation profile and an integrated luminosity of $5 \cdot 10^5\,\rm pb^{-1}$ over $5 \cdot 10^7\,\rm s$. The analog SEU rate has been interpolated for a latency of 127 in deconvolution mode with a first level trigger rate of $100\,\rm kHz$. A total cross-section of $4.36 \cdot 10^{-10}\,\rm cm^2$, which is 100 times higher than the cross-section measured with a $40\,\rm\sigma$ threshold, has been assumed to include fake signals of low amplitude. Tab.  shows the average SEU rates for inner and outer barrel sections of the CMS tracker. As mentioned above, these numbers are derived from the pion cross-sections and should rather be considered as an upper limit. Due to large uncertainties, they merely indicate the order of magnitude of SEU rates which one can expect at CMS.

Table: Extrapolation of the pion SEU cross-sections to CMS. Due to large uncertainties, these numbers only indicate the order of magnitude. The analog occupancy gives the probability of an analog SEU on a single channel.

Section	Avg. flux	Number	Mean dig.	Dig. SEUs/	Mean analog	Analog
	$\rm [cm^{-2}\,s^{-1}]$	of APVs	SEU time $\rm [s]$	time $\rm [h^{-1}]$	SEU time $\rm [s]$	Occupancy
IB	$1.40 \cdot 10^6$	14400	22.1	162.7	0.11	$6.88 \cdot 10^{-7}$
OB	$4.85 \cdot 10^5$	29232	31.4	114.7	0.16	$4.84 \cdot 10^{-7}$

Neither the digital nor the analog SEU rates pose a threat to CMS. A general reset with subsequent reprogramming of the APV chips should be performed periodically, and the DAQ software should mask wrong data from upset chips until the next reset. The number of analog SEUs is completely negligible, since less than one data sample in a million contains a fake hit. This can be regarded as a marginal increase in the noise background.