Confluencia del iusnaturalismo y el positivismo en los Debates acerca de la Doctrina Monroe.

The collisionless and turbulent nature of the solar wind facilitates the redistribution of the kinetic energy of its constituent particles via a wide array of complex interactions [123]. As a result, the local particle populations may become heated, and understand- ing the mechanisms through which this occurs is integral to understanding the nature of momentum and energy exchange in the system. Wave generation in the foreshock is driven by the two-stream instability (section (1.3.5)) of the continuous solar wind and the counter-propagating ion beam reflected at the quasi-parallel bow shock. A beam of suf- ficient strength will create a two-stream instability, generating a local maximum on the velocity distribution function that can sustain wave growth with phase velocities close to the velocity that corresponds to the bump maximum [124]. The waves receive energy from

the beam in doing so, and are said to bebeam resonant. Wave generation mechanisms in

the quasi-parallel foreshock are associated with particle distributions; FAB ion distribu- tions are associated with the generation of ULF fluctuations with fast magnetosonic waves whereas the diffuse distributions are associated with compressive fluctuations [76][60].

The existence of minor ions in the solar wind, in particular Helium ions, He++, may res-

onate with the left-hand mode found in the FABs, at frequencies ωci/2, where the power

is generally much greater. This interaction can provide an energy source for the magne- toacoustic cyclotron instability [125].

the solar wind itself. At 1 AU, the solar wind plasma shows correlations between velocity and magnetic field fluctuations that are characteristic of transverse Alfvén modes [126]. However, the phase coherence of these modes is generally destroyed prior to their arrival to the foreshock, and only a single observation has been reported to date [127]. Small den- sity perturbations are also detected in the solar wind; they are formed of both pressure- balanced structures in the corona and of fast magnetosonic modes [128]. The ion cy- clotron waves (field-aligned Alfvén waves with a frequency near the ion gyrofrequency) of equation (1.93) have been suggested as a possible source of solar wind heating and ac- celeration but detection of these modes in the solar wind is ambiguous [129].

The experimental delineation of modes generatedin situat the foreshock, in opposition

to those modes that are directly implanted into the foreshock via the solar wind, is im- portant to the understanding of wave-particle interactions and the channels of energy transfer in the system. Previous results based in the foreshock have made use of the wave telescope, or k-filtering, technique [130][131]. This is a technique based on a generalized minimum variance analysis (section (2.3.1)) that uses multi-station measurements to de- termine both wavenumber vectors and their associated wave power. Narita [132] used this technique to derive dispersion relations from Cluster data and identified estimates of the dominant modes and their associated dispersion relations, in the ULF domain[132]. It has been clearly demonstrated that these modes propagate upstream, in accordance with the proposed ion beam instability generation mechanism [133]. The unstable distributions may be abundantly found throughout the quasi-parallel shock, and the growth rates of the instabilities are on the order of 100s, with propagation velocities of the associated ULF

waves typically (50-100)kms−1. A continuous distribution of power would therefore be ex-

pected amongst the unstable modes [76]. Additionally, non-linear processes distinct from the ion beam instability, such as the decay instability of the Alfvén waves, or the modula- tion instability of the fast magnetosonic mode, may also be present and redistribute power on separate channels [134].

There are two main limitations of the wave telescope technique. Firstly, the technique requires measurements from three or more probes, ideally four probes arranged in a 3- D tetrahedron, to accurately determine wave vectors [135]. Secondly, the technique is sensitive primarily to the most powerful fluctuations at each wavenumber-frequency pair [136]. The work of this chapter is concerned with quantifying how fluctuating power is distributed amongst different coexisting quasi-coherent modes in the foreshock. Using simultaneous two-point measurements, the dispersion relations for three intervals that have differing macroscopic parameters, but similar ion distributions, are derived using a technique able to resolve multiple branches of the dispersion curves. The method involves

first rotating the magnetic field vectors from GSE coordinates to a frame centred on the wave propagation using the minimum variance analysis (section (2.3.1)). The wavevectors are then found by a statistical technique that characterizes the vectors by their associated powers at given frequencies (section (2.3.2)). The powers are then collated in a histogram of wavenumber and frequency pairs and a dispersion relation is formed. Crucially, this means that the technique introduced in this chapter is able to associate absolute powers to particular wavenumber-frequency pairs, a capability lacking in previously employed techniques. Multiple ensembles of measurements are necessary for the technique to work effectively. The frequency of the power maxima are then individually expressed in the plasma rest frame through the Doppler correction.