Tracking particles at fluences 5-10 $cdot$1E16 $n_{eq}$/cm$^2$

This paper presents the possibility of using very thin Low Gain Avalanche Diodes (LGAD) ($25 - 50mu$m thick) as tracking detector at future hadron colliders, where particle fluence will be above $10^{16}; n_{eq}/cm^2$. In the present design, silicon sensors at the High-Luminosity LHC will be 100- 200 $mu$m thick, generating, before irradiation, signals of 1-2 fC. This contribution shows how very thin LGAD can provide signals of the same magnitude via the interplay of gain in the gain layer and gain in the bulk up to fluences above $10^{16}; n_{eq}/cm^2$: up to fluences of 0.1-0.3$cdot 10^{16}; n_{eq}/cm^2$, thin LGADs maintain a gain of $sim$ 5-10 while at higher fluences the increased bias voltage will trigger the onset of multiplication in the bulk, providing the same gain as previously obtained in the gain layer. Key to this idea is the possibility of a reliable, high-density LGAD design able to hold large bias voltages ($sim$ 500V).