= Solution
For an <ultrarelativistic particle>, <relativistic beaming> concentrates the <synchrotron radiation> within an angle of order $1/\gamma$ around its instantaneous <velocity>. A fixed viewing direction in the orbital plane receives an intense signal only when the tangent sweeps through that direction. One <electron>, or one sufficiently short bunch, therefore produces one pulse per revolution, separated by $\mathcal T\simeq10.48\,\mathrm{\mu s}$. Several bunches produce the corresponding additional pulses per revolution.
The time during which the <velocity> points within that cone is of order $r/(\gamma c)$, but this is the \b[emission] interval. If $t_a$ is the arrival time at a distant detector,
$$
t_a=t+\frac{D-\mathbf n\cdot\mathbf x(t)}c,\qquad
\frac{dt_a}{dt}=1-\mathbf n\cdot\boldsymbol\beta.
$$
Near alignment, $1-\beta\cos\theta\simeq(\gamma^{-2}+\theta^2)/2=O(\gamma^{-2})$. Thus <synchrotron pulse compression> reduces the observed duration by a further factor of order $\gamma^2$:
$$
\boxed{\Delta t_{a,\mathrm{single}}\sim\frac r{\gamma^3c}
\simeq8.3\times10^{-18}\,\mathrm s.}
$$
A more explicit geometric estimate chooses the cone edges $\theta=\pm1/\gamma$. With $\omega=u/r$, $x=r\sin\theta$ along the line of sight, the difference in <arrival-time compression for a moving source> is
$$
\Delta t_a=\frac{2r}c\left[\frac{1}{\beta\gamma}-\sin\!\left(\frac1\gamma\right)\right]
\simeq\frac{4r}{3c\gamma^3}\simeq1.10\times10^{-17}\,\mathrm s.
$$
The order-one coefficient depends on how pulse width is defined; the robust scale is $r/(c\gamma^3)$. The usual central-cone estimate $r/(2c\gamma^3)$ gives $4.1\times10^{-18}\,\mathrm s$. These estimates agree on the attosecond scale and must not be confused with $r/(\gamma c)\simeq2.84\times10^{-10}\,\mathrm s$.<Synchrotron Radiation by Richard Fitzpatrick>[§12.22, equations (1979)–(1981): distinction between emission interval and detector arrival interval]{ref}
\b[Bunch qualification.] The source says only that the bunches are short, without their longitudinal <length> $L_b$. Different <electrons> pass the same emitting tangent at times separated by up to about $L_b/u$, with essentially the same path length from that tangent to the detector. The <bunch-length broadening of synchrotron radiation> means that the measured bunch envelope is the single-<electron> pulse convolved with the bunch's passage-time profile; its scale is generally at least of order $\max\{L_b/u,r/(c\gamma^3)\}$, with additional detector bandwidth effects. For example, a $1\,\mathrm{mm}$ bunch, very short compared with this ring, gives an approximately $3.3\,\mathrm{ps}$ envelope, much longer than the single-<electron> duration. No unique numerical bunch-envelope width follows from the supplied data. The pulse argument also presumes that the accepted $+x$ direction is tangent to the orbit; a direction far outside the orbital plane receives no comparable intense forward pulse.
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