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@@ -1802,6 +1802,12 @@ <h4 data-number="21.5.5.2" class="anchored" data-anchor-id="turbulenct-reformati
 <p>Indeed, electron reflection into beams which generate Langmuir waves is presumably possible only when in the supercritical quasi-parallel shock transition region the magnetic field changes from quasi-parallel to quasi-perpendicular on the electron scale <span class="math inline">\(\sim d_e\)</span>. Indications of such a change on the ion scale <span class="math inline">\(d_i\)</span> have been noted above at a number of occasions, but the detection of solitary structures in the electron plasma waves in relation to quasi-parallel shock transitions provides a very strong argument for this to be true on a scale which is well below the ion scale. Only if this is the case, there will be ample reason for electrons to become reflected and accelerated into beams from the transition region in a quasi-parallel shock. As we already noted, we may, therefore, expect that quasi-parallel supercritical shocks on the electron scale are not anymore quasi-parallel but change to become locally quasi-perpendicular, while on the larger ion scale they still remain quasi-parallel. Because of this reason high Mach number quasi-parallel shocks will be embedded into a diffuse high energy electron component that emits radiation.</p>
 <p>If this conclusion will turn out to be true, it will have important consequences for collisionless shock physics. Supercritical, collisionless, nonrelativistic shocks will, in fact on the electron scale, always behave quasi-perpendicularly, and it may be suspected that this conjecture will also hold for relativistic shocks though probably for other reasons (like the generation of transverse magnetic fields by the Weibel instability, which becomes dominant in relativistic shocks [see, e.g., Jaroschek et al, 2004, 2005]). This implies also that the true quasi-parallel shock physics cannot be properly elucidated when ignoring electron effects as is, for instance, done in hybrid simulations.</p>
 <p><strong>Simulations</strong></p>
+<p>We do already know from the observations that quasi-parallel shocks exist at small <span class="math inline">\(\theta_{Bn}\)</span> with their foreshocks being populated by a diffuse ion component that excites upstream waves and mediates the beam-generated upstream ion-foreshock boundary waves. The impossibility for this diffuse component of being entirely due to shock reflection in the quasi-perpendicular part of the shock, immediately proves that the quasi-parallel (or even the nearly parallel shock) must be able to reflect particles upstream. Hence, either a quasi-parallel shock is capable of generating a large cross-shock potential, or it is capable of stochastically – or nearly stochastically – scattering ions in the shock transition region in pitch angle and energy in such a way that part of the incoming ion distribution can escape upstream, or – on a scale that affects the ion motion – a quasi-parallel shock close to the shock transition becomes sufficiently quasi-perpendicular that ions are reflected in the same way as if they encountered a quasi-perpendicular shock.</p>
+<p>Observations suggest that the latter is the case, while observations also suggest that large potential drops occur in the large-amplitude magnetic pulsations (SLAMS) where they accumulate in the shock ramp [Behlke et al, 2004]. Hence, reflection of ions will be due to the combination of both effects, the electric potential drop and the magnetic deflection. In fact, this can be a quite complicated process for an ion passing across a number of magnetic pulsations, in each of which it is being retarded and at the same time deflected by a small angle until its normal velocity component is decreased sufficiently that a further deflection in pitch angle suffices to let it return into the upstream region.</p>
+<p>Early hybrid 1D simulations have already confirmed some characteristics of quasi-parallel shocks. First 1D hybrid simulations in an extended simulation box [Burgess, 1989] suggested that the reformation of quasi-parallel shocks is about cyclic and is caused by the impact of large-amplitude upstream waves. Scholer &amp; Terasawa [1990], using <span class="math inline">\(\theta_{Bn} = 20^\circ\)</span> and MA = 3.5 with an upstream ion thermal velocity <span class="math inline">\(v_{th,i} = V_A\)</span>$ (corresponding to <span class="math inline">\(\beta_i = 1\)</span>) in 1D hybrid simulations (with small numerical resistivity) showed that the reflected ions are not coming from the core of the incident upstream ion distribution but originate in the shell of this distribution, having initial velocities <span class="math inline">\(v \simeq 1.7v_{th,i}\)</span>. These ions escape from the shock quite far upstream and excite ULF waves with upstream directed velocity of <span class="math inline">\(\sim 1.3 V_A\)</span> at distances up to <span class="math inline">\(&gt; 300 d_i\)</span>, which are convected downstream to reach the shock. In this 1D hybrid simulation the only mode in which they can propagate is the compressive fast magnetosonic mode.</p>
+<p>These waves are in fact what in observations has been identified as pulsations (SLAMS) but is not yet recognized as such, here. During downstream convection the waves grow and slow down in the interaction with the foreshock ion component. When approaching the shock they generate a large amount of new reflected ions. These slow the incident ion population down and steepen the wave crest, which becomes the new shock front. In the time between the arrival of the compressive waves the shock is about stationary and develops phase-locked upstream whistlers which the arriving next wave crest destroys. From these simulations it could not be concluded what process produced the reflected ions, however, as 1D simulations among suffering from other eficiencies select only one particular direction of wave numbers and are thus not general enough for drawing final conclusions.</p>
+<p>The nature, generation and effects of the large-amplitude upstream waves have been further investigated in more detail in 1D [Krauss-Varban &amp; Omidi, 1991; Scholer &amp; Burgess, 1992; Scholer, 1993, among others], and in 2D hybrid simulations [Krauss-Varban &amp; Omidi, 1993; Scholer, 1993; Dubouloz &amp; Scholer, 1995]. Since shocks are three-dimensional, it is clear that two-dimensional numerical simulations at same resolution come closer to reality. However, they suffer from restrictions in size of the simulation box and simulation time. Since reality does not confront us with an initial state, large boxes and long times are needed.</p>
+<p>In order to identify a particular wave mode, the dispersion of the wave must be investigated. This dispersion relation depends on the frame in which it is taken, because the energy/frequency of a wave is not invariant with respect to coordinate transformations; in a medium moving with velocity <span class="math inline">\(\mathbf{V}\)</span> it is Doppler shifted according to <span class="math inline">\(\omega^\prime = \omega(\mathbf{k}) - \mathbf{k}\cdot\mathbf{V}\)</span>, where <span class="math inline">\(\omega(\mathbf{k})\)</span> is the dispersion relation in the rest frame of the flow. While the Doppler shift at high frequency is negligible, it completely changes the dispersion of ultra-low frequency waves at large Mach numbers.</p>
 </section>
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 <section id="parallel-shock-particle-reflection" class="level3" data-number="21.5.6">