Context :

Aims : The characteristic outer scale of turbulence ( i.e .
the scale at which the dominant source of turbulence injects energy to the interstellar medium ) and the ratio of the random to ordered components of the magnetic field are key parameters to characterise magnetic turbulence in the interstellar gas , which affects the propagation of cosmic rays within the Galaxy .
We provide new constraints to those two parameters .

Methods : We use the LOw Frequency ARray ( LOFAR ) to image the diffuse continuum emission in the Fan region at ( l,b ) \sim ( 137.0 ^ { \circ } , +7.0 ^ { \circ } ) at 80 ^ { \prime \prime } \times 70 ^ { \prime \prime } resolution in the range [ 146,174 ] MHz .
We detect multi-scale fluctuations in the Galactic synchrotron emission and compute their power spectrum .
Applying theoretical estimates and derivations from the literature for the first time , we derive the outer scale of turbulence and the ratio of random to ordered magnetic field from the characteristics of these fluctuations .

Results : We obtain the deepest image of the Fan region to date and find diffuse continuum emission within the primary beam .
The power spectrum displays a power law behaviour for scales between 100 and 8 arcmin with a slope \alpha = -1.84 \pm 0.19 .
We find an upper limit of \sim 20 pc for the outer scale of the magnetic interstellar turbulence toward the Fan region , which is in agreement with previous estimates in literature .
We also find a variation of the ratio of random to ordered field as a function of Galactic coordinates , supporting different turbulent regimes .

Conclusions : We present the first LOFAR detection and imaging of the Galactic diffuse synchrotron emission around 160 MHz from the highly polarized Fan region .
The power spectrum of the foreground synchrotron fluctuations is approximately a power law with a slope \alpha \approx - 1.84 up to angular multipoles of \lesssim 1300 , corresponding to an angular scale of \sim 8 arcmin .
We use power spectra fluctuations from LOFAR as well as earlier GMRT and WSRT observations to constrain the outer scale of turbulence ( L _ { out } ) of the Galactic synchrotron foreground , finding a range of plausible values of 10 - 20 pc .
Then , we use this information to deduce lower limits of the ratio of ordered to random magnetic field strength .
These are found to be 0.3 , 0.3 , and 0.5 for the LOFAR , WSRT and GMRT fields considered respectively .
Both these constraints are in agreement with previous estimates .