This thesis reports the design, construction, and the initial results obtained from a digital spectrograph for observations of radio burst emission from the Sun. One of the distinct advantages of radio spectral studies of the Sun during events such as solar flares, coronal mass ejections (CMEs), etc. is that it gives a straight forward estimate of the speed of the outflowing material into the outer atmosphere of the Sun and subsequently the interplanetary medium. It is well known that in the solar atmosphere, the electron density and consequently the plasma frequency gradually decreases with increasing distance from the center. Therefore in a time-frequency plane, the intensity of the associated radio emission should generally drift from high to low frequencies with time. From this, and from a knowledge of the height of the successive plasma levels in the solar atmosphere, one can deduce the speed of the outward moving disturbance. In this respect, a study of the radio bursts at decameter wavelengths is important since such radiation originates from the corona at heights ≥1.3 R⊙ (1 R⊙ = 6.96 x 10° km = radius of the Sun) from the center of the Sun, which are otherwise accessible only through the use of white light coronagraphs atop high altitude mountains and onboard space vehicles. The primary units of the instrument are (i) zero-crossing detector (ZCD), (ii) sampler and (iii) correlator. The function of the ZCD is to digitize the input signal waveform. In the present case, we use a one-bit quantizer, i.e., its output is either a '1' or '0' depending on whether the input is above or below the zero level, respectively. The digitized signals are then sampled at the Nyquist rate using the sampler. The output of the sampler is then passed through a set of shift registers, and finally fed to the correlator. The latter measures the correlation between the signals at its input as a function of the delay (introduced by the shift registers) between them. After successful completion of several static/dynamic tests in the laboratory, the system was moved to the Gauribidanur radio observatory (Latitude: 13°36’12”; Longitude:77°27’07”), and is presently used along with the existing radiohe-liograph to derive both the spectral and spatial information of the various radio emitting transient sources on the Sun, respectively. The R..F. signal (40-150 MHz) from one of the antenna groups of the ra-dioheliograph forms the input to the spectrograph. The signal from the field goes through a series of amplification and mixing operations to bring it down to an I.F. of 10 MHz with a bandwidth of 1 MHz, and then fed to the spectrograph. The present frequency range of the spectrograph is 40 MHz, and the data corresponding to the above band is obtained in steps of 1 MHz by switching the local oscillator through a GPIB interface, after each integration period. Each 1 MHz data is then Fourier tranformed to get its corresponding power spectrum. Successive data sets are then arranged in order according to the frequency of the local oscillator signal to get the spectrum corresponding to the entire 40 MHz band. The initial results obtained with our instrument are also presented.

This dissertation uses shocks to explain both the prevalence of radio synchroton emission and dust formation in classical novae, as well as the origin of fast radio bursts. First, we examine the radio lightcurves of nova V809 Cep and find that the peak brightness temperature exceeded 10⁵𝘒, an order of magnitude above what is expected for thermal emission. We argue that the brightness temperature is the result of synchrotron emission due to internal shocks within the ejecta. We then examine the radio lightcurves of seven novae with radio evidence for shocks (QU Vul, V1723 Aql, V5668 Sgr, V809 Cep, V357 Mus, V1324 Sco, PGIR20fbf) and IR/optical evidence for dust formation. We demonstrate that dust formation generally precedes the rise of radio non-thermal emission, and present evidence to suggest that shocks occur prior to the onset of dust formation but that the radio shock emission is initially being absorbed by a layer of photo-ionized gas ahead of the shock. We model the optical depth of the photo-ionized gas to demonstrate that the time required for the photo-ionized gas to become optically thin to radio frequencies can be longer than the time required for dust nucleation; thus, dust appears to form before the shock emission is visible. We further demonstrate that the radio spectral evolution in novae with no evidence for dust formation is markedly different from novae with evidence for shocks, suggesting that in novae without velocity or distance estimates, the radio spectral evolution could be used to constrain the presence of shocks. Finally, we demonstrate that novae with evidence for dust absorption are preferentially inclined edge, on suggesting that both shocks and dust form in the equatorial plane. Since internal shocks in nova ejecta are thought to lead to dust formation, localizing both phenomenon to the equatorial plane strengthens the connection between the two phenomena. We then use Particle-In-Cell (PIC) simulations to explore the synchroton maser instability as a potential mechanism for the formation of Fast Radio Bursts. Electromagnetic precursor waves generated by the synchrotron maser instability at relativistic magnetized shocks have been recently invoked to explain the coherent radio emission of Fast Radio Bursts. By means of two-dimensional particle-in-cell simulations, we explore the properties of the precursor waves in relativistic electron-positron perpendicular shocks as a function of the pre-shock magnetization σ ≳1 (i.e., the ratio of incoming Poynting flux to particle energy flux) and thermal spread Δᵧ ≡ 𝑘𝑇/𝑚𝑐² = 10⁻⁵−10⁻¹. We measure the fraction 𝑓𝜉 of total incoming energy that is converted into precursor waves, as computed in the post-shock frame. At fixed magnetization, we find that 𝑓𝜉 is nearly independent of temperature as long as Δᵧ ≲ 10¹·⁵ (with only a modest decrease of a factor of three from Δᵧ = 10⁻⁵ to Δᵧ = 10¹·⁵, but it drops by nearly two orders of magnitude for Δᵧ ≳ 10⁻¹. For our reference σ = 1, the power spectrum of precursor waves is relatively broad (fractional width ∼ 1−3) for cold temperatures, whereas it shows pronounced line-like features with fractional width ∼ 0.2 for 10⁻³ ≲ Δᵧ ≲ 10¹·⁵. For σ ≳ 1, the precursor waves are beamed within an angle ≃ σ -⁻¹/² from the shock normal (as measured in the post-shock frame), as required so they can outrun the shock. Our results can provide physically-grounded inputs for FRB emission models based on maser emission from relativistic shocks.