It has recently been discovered that the radar phenomenon PMSE (Polar Mesospheric Summer Echoes, [Cho and Röttger, 1997]), which occur in the summer mesosphere between about 80 and 90 km, can be weakened if it is affected by artificial electron heating. This weakening of PMSE has been observed with the EISCAT VHF radar at 224 MHz [Chilson et al., 2000; Belova et al., 2003], and the EISCAT UHF radar at 933 MHz [La Hoz et al., 2003]. The EISCAT heating facility [Rietveld et al., 1993] used in these experiments was run in equal and short on and off intervals (from 10 to 20 sec) and it was found in many cases, but not all, that the PMSE strength was rapidly weakened when the heater was turned on, and that it also returned rapidly [Belova et al., 2003] to approximately the pre-heater value when the heater was turned off again.
 Rapp and Lübken  showed that the electron density gradients within a collection of dust particles, which are a natural consequence if spatial density variations in charged dust are present [Havnes et al., 1984, 1990, 1992; Lie-Svendsen et al., 2003], will be rapidly smoothed if the electron temperature is raised by a considerable factor, such as is expected from artificial heating. When the heater is switched off, the electrons almost immediately cool to the neutral (and ion) temperature, and the electron spatial irregularities are re-established and the PMSE is strengthened again. In the observations by Chilson et al. , Belova et al.  and La Hoz et al. , all run with equal and short on and off intervals, the PMSE returns approximately to the strength it had in the former off phase.
 With a time dependent version of the standard dusty plasma (dust-electron-positive ion) model [Havnes et al., 1984, 1990; Verheest, 2000], Havnes  modelled the variations of the PMSE strength during overshoot heating cycles with the heater on for 20 sec and thereafter off for 160 sec. With dust, or aerosols, we here mean any solid particle (icy or mixed with e.g., metals) with sizes from about a nanometer and upwards. The PMSE modelling is based on the PMSE to be caused by scattering from many electron density gradients with characteristic lengths of the order of a half radar wavelength. In our case the electron gradients are within and are controlled by similar small dust density spatial irregularities, which we will call a dust cloud. The dust particles in a cloud are charged by electron and ion collisions and attachment, and the cloud itself will also be charged up and have a general electric potential V. Both the dust charges and dust cloud potential depend on the dust density and therefore on the position in the cloud, they also depend on the electron and ion temperature and their density outside the cloud, and on the ion mass. The potential V has its largest (negative) value in the centre of the dust cloud where the dust density is highest. At the summer mesospheric conditions, with its low temperature, the dust charges are low and predominantly negative with charge numbers normally somewhere in the range 0 to −4. The electric potential of the cloud due to the dust charging is also low, with a maximum value of the order of a few times the plasma temperature measured in eV, or around −.02 Volt. The electron and ion densities nα are Boltzman distributed in the cloud potential
Here n0 is the plasma density outside the dust, the plasma particle charge and temperature is qα and Tα respectively while kB is the Boltzman constant. The model also includes equations for a time dependent dust charging with plasma currents to the dust, and charge equilibrium. It is assumed that the plasma adjustment to the changes in electron temperature is short compared to the heating time. As examples of model results we show in Figure 1 two cases computed for a plasma density n0= 4 × 109 m−3 and an increase in the electron temperature from 150°K without the heater, to 390°K when the heater is on. We have used two different dust sizes as given in the figure. The dust density is nd = 109 m−3 for the case with particles of radius r = 10 nm and nd = 4 × 107 m−3 for the 50 nm large particles. These are values close to what can be observed in the PMSE region [von Cossart et al., 1999], and the values have been chosen so that the product ndr2 is the same for the two cases. The charging is by plasma attachment only. The relative PMSE backscatter is taken to be proportional to the electron density gradient in what we take as an average dust cloud. This will be a structure where at the center the dust density is nd, and at a distance of typically λ/2 from the center, the density for the cases in Figure 1 is reduced to 0.8 nd. The variation of the relative electron gradient (the varying gradient divided by the initial gradient) is not much dependent on the initial electron gradient but is mainly a function of the electron density, the dust size and density and the increase in electron temperature. For a calculation of the absolute value of the radar scattering, the absolute values of the electron gradients will be of importance. We have not considered such calculations. The different phases of the overshoot characteristic curves (OCC) in Figure 1 are indicated by the numbers (0, 1, 2 and 3). Initially the PMSE plasma is undisturbed with dust charges and plasma densities in equilibrium at the temperatures Te = Te = 150°K until point (0) when the heater is switched on, resulting in a rapid electron temperature increase [e.g., Kero et al., 2000; Belova et al., 2001]. The main effect of a temperature increase can be seen from Equation (1) which shows that the electron density profile will be flattened and its gradient therefore reduced. This results in the PMSE power drop from (0) to (1). If the electron temperature increase is large, the exponential term in Equation (1) will be ∼1 and the electron density will be approximately constant through the cloud at point (1). The magnitude of this drop is therefore mainly determined by the increase in the electron temperature. During the recovery, or heating phase (1–2) the dust will be charged more negatively by the electrons which, with their increased energy and increased density within the cloud, can charge the dust to a negative charge considerably above the charges at and above (0). This increases the potential V to a more negative value, and Equation (1) shows that this will to some degree restore the electron depletion at the dust cloud centre and cause some recovery of the PMSE. When the heater is switched off at (2), and the electron temperature falls back to the value of Te= Ti, the increased dust charges and increased potential V at (2) compared to its value at (0) and (1) will lead to a stronger electron depletion in the cloud centre at (3) than before the heater was switched on. This leads to a larger electron gradient also and consequently a PMSE overshoot where the PMSE strength is larger at (3) than at (0). After (3) the PMSE dusty plasma relaxes back to its undisturbed state, in a process where the dust is gradually losing negative charge until it reaches the lower equilibrium charges for Te = Ti ∼ 150°K.
 The reason for the long off phase in the model calculations and in the new observations, was to give the dusty plasma sufficient time to relax back to its undisturbed conditions, or to allow horizontal wind transport to bring undisturbed dusty plasma into the radar beam. Model calculations show that with equal and short heater on and off intervals, the dust particles continue to be charged up by subsequent heater on phases, to a saturation value where de-charging during an off phase balanced the charging during an on phase, or alternatively to a maximum charging set by the time for horizontal winds to transport new PMSE dusty plasma into the radar beam. For the former high duty-cycle heater cycling, the difference in electron densities in subsequent off phases will be small and give the appearance that the PMSE returns to its undisturbed value as soon as the heater is switched off. In fact, the electron density gradients in the saturated off intervals will be considerably stronger than for identical PMSE conditions, which are not affected by the heater. The strength of the PMSE during saturated off phases will therefore in general be stronger than that of an identical undisturbed PMSE. The difference in PMSE strength during saturated on and off phases will therefore be larger than the difference between the strength of an undisturbed PMSE and its reduced intensity as the electrons are heated. One of the advantages of the new cycling is that if the heater is allowed to operate on undisturbed PMSE, the difference in PMSE power between the phase just before the heater is turned on and the phase just after it is turned off is maximized. The relaxation time, and other details of the overshoot will lead to additional information on the PMSE conditions.
 An observational campaign looking for and finding the overshoot effect was performed on the days 27 June, and 1 and 2 July 2003. The data are still being analysed but we here show some examples of the overshoot, which was repeatedly seen during the three hours we observed on the 2nd of July 2003.